I could live with it in a single player run, where I don't imperil my party

BTW, wouldn't high STR partially substitute for the unarmed strikes used in the flurry of blows? If I remember correctly, your base unarmed damage is 1+STR and it works same in BG3 I think. That means the damage will be flat 6 by level 12 which is fine when compared to d10 dice the usual monks get.
[...]
What I am planning is:
- Set initial stats as 17 (STR), 8 (DEX), 15 (CON), 12 (INT), 12 (WIS), 10 (CHA) after the racial bonus applies
- Take Heavily Armored at level 4, boosting STR to 18 and solving the AC problem
- Take Heavy Armor Master at level 8, boosting STR to 19
- Take ASI at level 12, boosting STR to 20 and CON to 16