So, I am DMing for a group of players that is irritated with the traditional method of initiative - making Dexterity even more important, providing metagaming opportunities, etc. Is there a good initiative alternative that provides a solution to these problems? I looked in the Dungeon Master's Guide and a few other sources and found a few, but they all seem to have problems:

Side-based initiative (In a nutshell, each group of allies roles once and all act together): Fast, but more or less removes the idea of initiative and I don't want the encounters turned into repeated "I hit the monster, then the monster hits me"

Initiative Score/Passive Initiative (10 + initiative modifier, no d20): Makes the initiative less random, but metagaming would probably be even more prevalent

"Keep your initiative secret" (don't reveal your initiative, DM counts down from 30 and you take your turn when your initiative is called): I think this would make the players feel like they are keeping secrets from each other, the Cleric plans to heal the Fighter because he has an initiative that is probably next but the Fighter wants to run

Speed Factor: This got me really interested, what with replacing Dexterity and having a good system that makes attacking with Daggers faster than attacking with a Battleaxe, but the calculations for initiative would be really slow

Wisdom Initiative: This seems like a low-quality change that doesn't really replace the initiative system, just uses another ability score. Am I supposed to sit down for a session and say "By the way, Initiative uses Wisdom now"?

Have any of these options worked well for you?

Go around the table in order.  Before each sessions define a position for each player based on where they sit at the table.  Make a random roll or draw position number to determine the "head of the table".  That person goes first, and then you move down the list in order. The DM spot at the table represents the monsters turn.  If you don't want all the monsters to go at the same time, then remove the DM from the table order and just have the monsters act in an order in between different players' turns (i.e. after every second player two monsters can take a turn). 

This takes away all issues the table may have with metagaming and stacking DEX, and leaves the order of combat as a random element that the DM rolls for each encounter.  If they don't like using the physical position at the table, or you play online, then find a random generator online (or do a draw of names form a hat) before the session to define everyone's table position.  This should keep the position order different in between sessions. 

An advantage of this is that when in non-combat scenarios you can end chaotic discussions by running through the table order: 

DM: "Okay, you are in the room and Kobolds are dead; Position one, what do you do?
Position One: "Search the room for secret passages"
DM: "Make a Perception check.  Position Two, go."
Position Two: "Loot the bodies."
DM: "Anyone help *Position 4 raises hand*. Ok, role Investigation with advantage.  Position 3, go"
Position Three: "I pass."
DM: "Position 4 you took the Help action, that is your turn.  Position 5, go"
Position 5: "If there are glyphs and markings on the wall I would like to study them otherwise, I want to drink a healing potion."
DM: "Nothing on the wall to study so roll for your healing.  Position One, you are up again...."

If you want the effects of secret initiative without requiring forcing people to keep secrets, a card-based randomizer works. Just give every character, and every monster that has a distinct initiative, a card. Shuffle cards together, play them one at a time, and that's whose initiative it is. On subsequent turns, either reshuffle, or use the original order and accept that people will take advantage.

If you don't want to deal with remaking the deck every encounter, just have fillers. Say, your deck is "player 1, player 2, player 3, player 4, monster group 1, monster group 2, monster group 3, monster group 4, monster group 5, monster group 6", and if you draw a card that doesn't correspond to anyone... discard and draw a new card. This has the side benefit that the players might not actually know how many monsters there are.

I liked the playing card system from Savage Worlds. I think it could translate well to D&D. You could say you get 1 card for each point in Dexterity and take the highest. If you get a Joker, it gives you advantage on all attack rolls, skill checks, and ability checks that round.

I have considered changing up initiative but I'm worried about slowing combat be having to calculate it. The style based on action speed feels the most thematic and tactical but calculating it every turn would definitely slow things down 

Dragonbane has a nice system where the players and monsters draw cards and do so every turn so the initiative order changes, not sure how you'd integrate dex bonuses to this unless you just draw the card and apply it straight to the result?

I've played with the initiative system from Fate before, which would have been fun if my party wasn't so big. Basically - one person goes first (gotta determine that person somehow), and then they decide if they want an ally to go after, or an enemy. 

The initiative will default to back-and-forth between ally and enemy, but for every time they choose to give the next turn to their ally, the enemies get another turn in a row as well. Can make for some interesting metagame opportunities of risking lots of enemy attacks in order to justify a big payout. Of course, there should be a cap of some kind for how many times in a row allies can "pass" to each other.