Sounds like something a custom subclass could be focused around, though.
Way of the Iron Fist has a nice ring to it.
But let me see what I can do without homebrewing first.
if you had a lvl of fighter lets say and had like a great sword you could use those to get some damage back
I believe the only 3 heavy armor are fighter, paladin, and cleric.
Paladin with Divine Favor would work well if I went Nick + Flurry, but lack of slots wouldn't let it keep uo.
Cleric can also use a greatsword. Healing Word is nice as a backup, but I don't see much use for cantrips. No good synergies.
So yea, Fighter 1. With defensive fighting style to really lean into the Iron monk theme.
biggest issue is that your unarmed damage will drop from a 1d6 + dex to 1 + str
There is Tavern Brawler, which makes it 1d5 (including the reroll). No scaling, but something.
Oh, Magic Initiate Druid, getting Shillelagh. That will be a die ahead most of the time. And Mending (Iron bending), and Longstrider.
You could also focus on a grappler build, being more about control than damage.
If I have the AC, I might as well keep enemies nearby.
Flurry of blows can easily be a grapple + trip.
The shadow monk still gets its full suite without skipping a beat wearing armor, so that's a good choice
Good call.
So..
Cast Darkness
bonus action Flurry to grapple+topple
They have disadvantage against high AC
They can't see to target me with most spells.
Evasion helps against AoEs.
And if they do hit, get a big damage reduction, with Heavy Armor Master more than making up for the lower Dex.
Then proceed to smack them with my d10 "Iron" club.
Oh, and be a Goliath so I can grab larger creatures and move quicker.
And make sure my allies have stuff like blind fighting, Devils sight, or can cast Clouds of Daggers.
That looks pretty solid to me.
You also give up all that wonderful bonus speed
That seems the be the biggest downside.