I'll have to second the notion of supporting unarmed fighting as a non-monk.
Tavern Brawler by RAW gives improvised proficiency, 1d4+str unarmed damage (instead of 1+str base) and allows bonus action grapple after unarmed or improvised weapon hit. Since grapple isn't implemented the secondary property is not that useful and the double str the BG3 version gives is better than the default after 16str and keeps a lot better after so there doesn't need to be too many changes there.
Unarmed Fighting style of fighter would work, making unarmed attacks 1d6+str, 1d8 versatile.
Other than that, I'd suggest adding grappling as is, reduce enemy movement to 0 and prevent them from standing up. No need for any particular animations and should be simple enough. That combined with properly implemented Tavern Brawler might make a brawling character viable. Though would require a fighter level for all non-monks to function.
