I know a friend who was into heavy lifting and still is, but who's been training for MMA since the last 3 years and from what i hear, he is extremely successful (as an amateur).
Since then, in addition to the basic lifts which he trains with a working max of 85% of his lifetime PRs in a rep range of 5-10, he does superheavy partials for high reps on the same basic movements and then heavy BB cheat curls (in place of any other bicep work), and he trains the Turkish Get Up like it was the last lift on earth. He has worked up to a TGU with a 100 pound sandbag (both arms).
For "assistance work", lots of pull a parts and "crawls" (bear crawls, leopard crawls, baby crawls). For his ab work, he relies on the AB wheel, side planks and standing and kneeling cable crunch and honestly any kind of "core" movement that he can test himself.
He trains his grip with levers and plate pinches.
His coach promised him "Train your core and stretch your hip flexors and hamstrings three times as often and you'll be shocked how much of your bench press strength carries over to a fight"
Since you're not looking to be a professional fighter, incorporating some of these should help you "use" more of your raw strength in real life.