So I think Barbarian suits your purposes for the big things you are looking for, and working with a subclass is a lot simpler than building a new one. I think Raging (with the standard resistances) give enough to Strength checks and standard resistances to cover the STRONGer than usual character, so Barb it is.
The other Barbarian subclasses get a combat feature at 3rd, exploration at 6th, and interaction at 10th. (look at WotC's Modifying Classes article). I'm making a few assumptions below, correct me if I am mistaken.
At 3rd level (or even 1st if you really want), give Marital Arts/Tavern Brawler (copy from Monk, just make sure fists are not better than martial weapons until higher levels, if ever). Get rid of Finesse and make them d6. Keep it in line with weapons and you're good.
At 3rd, give Absorb Elements. Honestly, looking at it I think just having it as-is while the Barb is raging is good enough. It's using your reaction and adding one resistance and a d6 damage for one turn on one attack. Compare it to the Bear totem's resistance, which is more defensive but always on while raging. This also stacks well with the Reckless Attack feature.
One thing you might want to do is scale it the same as your Martial Arts. If Martial Arts start at a d6, so does Absorb Elements. Then at level 5 they both go to d8, then at level 11 they are a d10, level 17 is d12.
If the damage seems too low, then change it to 1d6 at 3rd, 2d6 at 5th, 3d6 at 11th, and 4d6 at 12th (same progression as casting at a higher spell slot).
The Bear totem and Goliath racial trait also have higher drag/push/pull for utility at 6th that might fit your vision that you can copy.
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