Do lower control arm reinforcement plates actually work?

I plan on adding tabs of the same thickness down the side of them and plug weld through the floor, more like the original frames.

Yeah but the original frames are spot welded every 1-1/2" to 2" or less for the their entire length. You'd have to add flanges to pretty much the whole length of the subframe connectors to do that, and it's not like the connectors are flat on top for the whole length. I mean, it would be easier welding flanges to the top of the connectors while on the ground, right side up, than seam welding the connectors to the floor under the car, but I still think you're underestimating how much work it would be. A couple of tabs here and there wouldn't cut it.