The pace of play and scoring issue rings true with me, but not sure why.
I agree with Lou that playing faster gets you in a rhythm that seems to help me hit quality golf shots.
I recall playing Troon in Scotland with an elderly gent, and we finished in 2.5 hours, and I played well. Hard to tell exactly, because he was all about match play and we picked up if we were out of the hole. Of course, it meant the tee ahead also had to be open to take advantage. I didn't feel I took any less time than normal.
At Royal Melbourne, my ex and I also played three times over two days, also in 2.5 hours, and I shot low 80's, about my then normal "good" score. One round, we followed the ladies league and barely kept up, despite our two vs. their foursomes.
Stateside, I like to think I play fast enough, like when I get the first tee time off. I attribute most of that to "cart sense" of not just watching my cart partner play, and then start selecting my club. I drop them at their ball and drive to mine. The key being ignoring other shots by simultaneously getting ready to play (when out of line of flight and vision) It seems to me my overall speed is (assuming constant cart behavior) is more affected by course length. When I drop to 6300 or below, I hit many more greens, play fewer shots, etc.