Stick with the powerlifting style benchpress. Do supplementary higher rep/lower weight dumbbell benchpresses afterwards.
As you figured, benching with arched back has its benefits:
There is one major drawback:
So, should you do flat back bench pressing instead of with arched back? Personally, I don't think so. The best way to get better at a specific movement is to train that movement. With flat back, you do not train how to utilize leg drive. You do not train the proper bar path or how to raise the touching point as high as possible.
But you still don't get the benefit of a full range of motion! With a lowered back, the bar goes a bit lower and your pecs get more stretched (which is questionable anyways). But once at the top, the difference is minimal. You could narrow the grip to extend the range of motion, but this gets you further and further away from the original movement, losing specificity.
Theoretically, it might be better to do your arched back bench press with dumbbells as you can maintain the same form while doing the full range of motion. But doing a 1x5 benchpress with dumbbells at your strength level is just not practical. Even if it was, it still lacks specificity - the limiting factor in what you can press with dumbbells would probably be stabilizer muscles that barely get activated during barbell bench press. Still not optimal.
So here's what I would do: Keep doing arched-back bench presses on Tuesdays and Fridays, as it helps you getting better at arched-back bench presses on Tuesdays and Fridays. After that, throw in some supplementary high-volume dumbbell work, like 3x12 dumbbell benchpress. Your upper body is already tired from the 5x5 / 1x5 sets, so stabilizing muscles are less likely to be the bottleneck now. That'll maximise your strength gains.