With two layers, just bolt it to the plywood, through both layers. I use a squat/bench combo rack and I have not had movement issues (yet). If it does start to wander, I'll just put two screws through the base into the triple layer floor and it wont move anywhere.
You won't need a frame if you screw the plywood together. Don't use glue, you won't be able to pull it apart and move it when you win the lottery. You are going to screw it together anyway, so why spend more money.
Red Barn sell the smooth sided mats. One other factor is that the ribbed mats (yes, they are annoying) are often smooth on one side, so just use them turned over.
My deadlift area is 116cm wide. Collars on a proper barbell are 1.31m apart, which sounds a bit tight but when deadlifting you don't get much lateral shift. If you are doing olympic lifts, they tend to fly about a bit, but you are usually using bumpers for that so hitting the timber is not a problem.
I levelled my garage floor so for 2/3 of the floor area I have a layer of plywood as a base on the levelling wedges then a layer of 10mm then 20mm plywood.
In a commercial gym, the platform sits alone on the floor and may wander a bit. But mine sits of a floor wedged in on three sides by the garage walls and all screwed together, so it's one huge unit. It ain't going nowhere. A power rack screwed into two layers of plywood ain't goin' nowhere, so no need to drill into concrete. If your rack was on the concrete and the platform placed around it, that may require anchoring, but why do that. Just screw it into the plywood and it won't move.