Quote from Chicken_Champ >>

I'm not sure where your human + stats factor in, what feat you took at 4, etc... but if I understand correctly you're already a Barbaria (Zealot) 5, and the DM is open to you moving some stats around. If so I'd recommend you do something SUPER weird :) 

Monks lose a lot from wearing armor... but they don't lose everything . Put on armor and you lose the monk unarmed attack damage dice modifier (not a big deal if you're using something else), the unarmored movement speed bonus (not a big deal if you don't care about that), ability to make an unarmed attack as a bonus action (not a big deal if you have a different way to make a bonus action attack, or other use of bonus action), ability to attack with monk weapons/unarmed attacks using dex instead of str (not a big deal if you want to attack with Str)... but every OTHER monk base ability isn't affected by armor/shields, and most of the subclasses aren't either. 

Allow me to propose Barbarian (Zealot) 6/Monk (Sun Soul) 14. 

Be a Mountain Dwarf (to fit with using a Thor hammer, and to squeeze a lil bit of extra Stats out. Also, bonus proficiecies would theoretically let you drop Barbarian entirely for a pure monk armored monk? :p )

Stats at level 6 (Barbarian 5/Monk 1): Str 18 Dex 14 Con 14 Int 8 Wis 14 Cha 8

Feat at Barbarian 4: Tavern Brawler (+1 Str): lets you still punch things while armored if you so choose and not have complete noodle fists (since you won't benefit from martial arts whenever wearing armor). Also it's just generally a fun feat, and gives you a +1 to a stat you want anyway. Could just as easily be Squat Nimbleness or Athlete, if you'd prefer. 

ASI's at every other level: +2 Str at monk 4, +2 Wis at Monk 8, +2 Wis at Monk 12. Wisdom will give you better monk DCs, which helps with stunning strike and your spell like attacks. Alternatively, you could pump dex for better radiant bolts and take off your armor and play more of a real monk, but plllbbbbb that's boring and gives you poorer AC and thematic identity!

What'd you lose from not going Barbarian 20? Probably +1-3 better armor class at the very highest highest levels (but you have better AC at low/mid), fewer rages, slightly less damage per hit while raged, your zealot inspiring shout at 10, the zealot undying rage 14, better crits, better str checks, better hit points, advantage on initiative rolls. 

What'd you gain from picking up Monk 16? Well, there's the general monk goodness which is probably too much to list but I will anyway:

• If you're ever naked, you rock!
• Dodge, Disengage, or Dash as a bonus for a ki point
• Deflect missiles
• Slow fall to jump off cliffs better
• STUNNING STRIKE!!!
• Evasion!
• Purge frightened or charmed as an action
• Run across water/up walls
• immunity to disease and poison
• speak all languages
• HAVE ALL SAVES

But you also get some cool stuff from sun soul!

• You get a d4-d8 30 foot radiant damage laser beam that you can make as one of your two attacks during an Action using your (admittedly mediocre) dexterity; if you do use one of your two attacks for it, then as a bonus you can fire it two more times! Kind of makes up for it having a -2 to hit compared to your melee hammer strikes. 
• You can Burning Hands as a bonus action after an attack
• You can throw a light bomb as an action

Other than cool features from two classes, where is the Barbarian + Monk synergy? Well, there's isn't a ton, except:

• This is one of the few ways you can use spell-like effects (laser beam, light bomb) while raging, because otherwise rage stops spellcasting (and indeed it does stop your Burning Hands bonus action)
• Picking up stunning strike is pretty cool for any melee class, it lets your warhammer wallops really carry some weight
• Barbarians don't have a ton to do with their bonus actions. Pumping yourself up from 2 attacks to 4 attacks is pretty nice, even if they don't hit as hard/as reliably. Plus, they're ranged and radiant, which is a plus!
• Evasion saves a lot of hitpoints, and synergizes nicely with your barbarian Danger Sense
• Rage also saves a lot of hitpoints over a similar-AC pure monk. Despite the lower hitpoints than a pure Barbarian, you're probably a little tankier than both (you could be really REALLY tanky by taking Long Death monk instead of Sun Soul, but that wouldn't really fit your "i want to be a caster" angle). 

It's probably not the most optimal. But it requires a lot less fiddling than a 4-class character, and comes online basically at 8th level once you get to pick your monk subclass. 

 I like you ideas! I may try this in a different campaign 

I am working on an Eldritch Invocation (based on the UA iterations) let me know what you think.

Thor's hammer:
Prerequisite: Thor patron, pact of the blade feature

Thor allows you to use his hammer as your pact weapon. The warhammer you create has the thrown and return properties.
When you hit a creature with a melee attack with Thor's hammer, you may expend a spell slot to deal an additional 1d8 lightning and 1d8 thunder damage per spell slot level. The creature must make a strength saving throw or be knocked prone.

I would say just have it do 1d12 thunder damage (God of thunder) and have the damage dice scale with the spell slot level used.  Otherwise if you are using this later in the game you won't be getting much out of it.

While still typing I might also suggest, keeping the lightning damage and have both scale with the spell slot used but drop the dice to d6 for each.

So later on it would be 10d6 plus knockdown with a 5th level spell slot.  This would be similar to the damage you might get from an actual spell.  Something to consider at least.

Quote from HeroZero >>

I would say just have it do 1d12 thunder damage (God of thunder) and have the damage dice scale with the spell slot level used.  Otherwise if you are using this later in the game you won't be getting much out of it.

While still typing I might also suggest, keeping the lightning damage and have both scale with the spell slot used but drop the dice to d6 for each.

So later on it would be 10d6 plus knockdown with a 5th level spell slot.  This would be similar to the damage you might get from an actual spell.  Something to consider at least.

 I went with 1d8+1d8 to match the UA Eldritch Invocations that are similar at 2d8 per spell slot level.

What UA eldritch invocation?  I didn't see anything in the latest set...  But you have to think you have the knockdown as an added effect to the damage (that can be very helpful).

Quote from HeroZero >>

What UA eldritch invocation?  I didn't see anything in the latest set...  But you have to think you have the knockdown as an added effect to the damage (that can be very helpful).

 The list of UA Eldritch Invocations 

https://media.wizards.com/2017/dnd/downloads/20170213_Wizrd_Wrlck_UAv2_i48nf.pdf

oh, from two year old UA...  I was expecting something more recent.