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I would usually start off a warm-up with some general activity to wake up the system and warm. If I was benching, I’d probably want to see the shoulders moving, since that’s the main joint of interest here.
As far as specific prep for the bench, you say you do four fairly light warm-up sets. You might have better results with more progressive warm-up sets. I usually start with a bajillion or so reps with the empty bar, just to start grooving the technique, then slowly progress it up to my working weight. It kinda depends on what kind of time you have to work with, but if I was planning on doing 6×2’s (some fairly freakin’ heavy loading), I’d probably check out at least six warm-up sets.
This might be why you’re feeling that last set is the best one, simply because your technique is finally online and you’ve finally got the system completely fired up. That said, sometimes that last set is the best just because you’ve been practicing like a boss. In general, even though you’re fatigued, you’ll probably be at your technical best a little ways into the working sets.
Treat your benching as much like benching practice as skill training. Extend your warm-up, get a ton of practice reps in (with adequate rest, and performed sub maximally), and I think you’ll see good results.