So, I am trying to build a good Tank, one thing I have noticed is that you Need at least 15 Strength to wear heavier armors or at least 13 to meet multi classing where some of the best builds come from, You need CON for a good HP pool and then usually one other Stat CHR for Paladin, INT if you go the Artificer route. But naturally this leaves DEX as your weakness. I can do a build that guarantees to bolster saves with a WIS of 10 and a DEX of 10 but then my weakness as I have seen in play testing is Initiative. You're late to the party a lot of the time and it takes a few turns to get mobs taunted or compelled to you. I don't care about damage output as that's not the roll for this character its all Damage Mitigation and Damage Absorption or Deflection.

Samples:

Tortle race with 4, Oath of Crown Pally to start with 3, totem Barbarian. Here I am just meeting the STR 13 req for multiclassing and I am boosting DEX in my first ASI. Use Rapier and Shield. With Racial Stats and an ASI Boost my DEX 16 at this point. AC is not an issue until higher levels. This handles the DEX problem but now I'm spreading Stat points between, DEX/CON and CHR

Vhuman with the same but I leave DEX at 10, boost STR only needs to be 15 to get Plate Armor, again don't care about damage output. in this build the stats are a little more even but I don't really need to worry about STR I can concentrate on just CON and CHR but I am a slave to the die roll on Initiative. Hence the Late to the party sometimes.

Both of these approaches give me advantage and in some cases modifiers to weak saves like WIS and DEX as not all damage is from weapons. I know I am going Oath of the Crown Pally and the Bear Totem barbarian as a minimum. I know there is the option of Ancestral Guardian but I am less interested in penalizing mobs for attacking my party and concentrating on a Tank that can really take that beating. I am also not interested in the Moon Druid HP Wild Shape approach. I guess my Main Question here is I need something that can elevate that Initiative problem? 

EDIT: I guess I could take Alert Feat at level 4 for Vhuman as he is using Heavy Armor Master at first level. This would push back other ASI stat Boosts and I need to work the Tough Feat in there somewhere.

Sounds like your problem is forcing a build rather than game mechanics. But, I'll try.

So you want to tank, but not draw attacks? Be a damage sponge instead of damage dealer, but not interested in tripling your HP total? Play strength based build, but maximize dexterity? Wear heavy armor as a barbarian turning off most of your rage bonuses?

Why even bother with heavy armor? As a barbarian, getting CON and DEX up will make unarmored defense as good or better anyway, and you already want this stats high based on your concept. If using point buy, set your abilities to 12 15 15 8 8 13, put a +1 in strength to multiclass, a +1 in DEX and CON so they are both +3, and a +1 in CHA to round it off. If variant human, consider the sentinel or tough feats at level 1. You should have 18 AC with a shield. It's not plate level, but not bad.

If I wanted to build a good Tank I would personally go either straight Barbarian, or straight Paladin, or an Eldritch Knight Fighter with a teeny tiny 2 level dip into Paladin. The thing is, to be an effective Tank you need to be a scary enough damage dealer to draw the heat from the enemies, and take the hits. If you don’t deal fairly significant damage they can afford to ignore you, and if they can’t hit you either they will ignore you. The harder you are to hit, the more you need to be scary enough to make them focus on you anyway. Either Paladin or Barbarian on their own is a strong tank, one because of their AC, the other because they can just soak that many hits, and between Smites and Rage they are both really solid damage dealers.

My third pick, the Eldritch Knight with the dip also fills the role of tank, and for the same reasons. They can focus their spell selection on Abjuration magic, most of the best 1st-level Paladin spells don’t even need Cha so it can be the 13, just barely enough to qualify for the multiclass. And the Paladin’s Smite ability adds damage threat on top of Action Surge, and their inherent Second Wind adds to their tankyness.

I hope this helps.

Max dex with studded leather armor only puts you 1 AC point behind full plate. Then you still get all the benefits of a high dex (initiative, dex save, etc.) plus, you’ll be pretty stealthy — sneak up on them. 
I just a couple of months ago finished a campaign at level 13 with a halfling dex paladin. 3 feet of righteous tanking fury. Worked beautifully. And the only magic I had was + 1 leather and a +1 short sword. 

There is also the Alert feat - +5 to initiative, not surprised and opponents don't get advantage if you can't see them.

I'd also add that a "tank" doesn't need heavy armor. The difference between light, medium and heavy armor is only 1AC point. Studded leather with 20 dex is 17, Half-plate with 14 dex is 17 and plate armor is 18.

"Tanking" also doesn't really work in 5e with the exception of the Armorer Artificer with Guardian Armor as ArntItheBest mentioned. Compelled Duel just isn't a very good use of a spell slot most of the time given all the conditions on it and the save every turn.

In terms of Armorer Artificer spell choices though, the go to spell at level 5 is Blur (2nd level spell) and at level 9 it is Haste (3rd level spell). The Mind Sharpener invocation is a very useful one for an artificer trying to maintain concentration on a spell.

Was going to say battle master fighter prot style makes a very good tank too. between being able to help your party members by giving baddies disadvantage. You have the different maneuvers to add to your AC/party members AC Like bait and switch, or ones to slow your foes like Trip, Maneuvering attack, Goading attack, or even evasive foot work to help your own AC with out using a attack/bonus/reactions action.

You can build tanks out of alot of things in ways and do not need to multi class all the time or try to mid/max or build the most optimal build out there.

Quote from David42 >>

"Tanking" also doesn't really work in 5e with the exception of the Armorer Artificer with Guardian Armor as ArntItheBest mentioned. Compelled Duel just isn't a very good use of a spell slot most of the time given all the conditions on it and the save every turn.

Was going to raise this same point, though Ancestral Guardian Barbarian can also do it a little bit for free.

What you get out of tanking is going to depend heavily on your DM, because there aren't many ways to force an enemy to attack you instead of an ally, and even the options that exist are mostly disadvantage rather than a real block, or things like Reckless Attack which should encourage enemies to attack you, but which your DM may ignore.

There also isn't really much in the way of area control that martial characters can do; if an area is 15 feet wide then you can at best maybe get an opportunity attack, which you can double down on with Sentinel (to stop an enemy in its tracks), but that only works for one enemy, against a group the rest can now freely move past you like you aren't even there.

So the first thing you should do is talk to your DM about what you want to get from tanking; I'm currently playing a character in a campaign who's a Fighter/Barbarian and very much built to take damage, but she only really has Reckless Attack (and a somewhat low AC 16) to encourage enemies to attack her and her mountain of Raging Bear Totem hit-points. What I do is work with my DM to describe what she's trying to do so that he knows that my intention is specifically to block a doorway and not let anything past to the squishier/wounded party members, or when I fight beside an ally I might specifically be trying to give them an opening to escape, so I'll describe that, this way if the ally disengages then the DM knows my intention was for the enemies to fight me instead (though whether all of them do or not is still up the DM to decide or roll for).

This is a big part of how tanking currently works in 5e, and maybe how it's supposed to work, though WotC never really go into a lot of detail about how you're meant to run enemies with these kinds of things in mind. Otherwise if you go purely on mechanics you need control casters to really truly tank.

Cavalier Fighter is a dedicated tanking subclass.  You don't need a mount for any of it's good tanking abilities.

My favorite tank is a shield using Ancestral Guardian Barbarian starting with 16 str and 14 dex who rarely uses reckless assault.

Decently high AC + lots of hit points + damage mitigation + agro mechanics = very effective tank.

Take the Fey Touched feat and pick up the Gift of Alacrity spell. +d8 to your Initiative for 8 hours. 

Doubly good if youre going the artificer armror tank route since youll have spell slots to cast with extra times if needed. 

Speaking of, the Psi Warrior is a fun dip for an Armorer tank. Gives you a ranged TK ability to dampen damage allies take. Pairs since you have juiced up int for this build anyway.

For low level, 1 level forge cleric with 3+ levels battle master fighter. Go Vhuman for str and con along with heavy armor master. Defense fighting style. Get the bait and switch and goading attack for a ac boost and taunt ability. 

AVERAGE AC (INCLUDING D8 SUPERIORITY DIE,  PLATE, SHIELD OF FATH, SHIELD): 27.5