I cut polycarbonate all the time. I use this bit:
https://www.toolstoday.com/v-13807-hss1621.html
It’s 3/16" diameter. They make it in 1/8" and 1/4" too. I feel like 1/8" might be too small a diameter for chips to clear out of the slot, but I could be wrong.
I’d cut 3/8" in (3) 1/8" passes. I leave tabs on the parts, then use flush cut nippers to (easily) cut the parts out of the sheet, then flush cut the tabs off.
I’d hold the material with double sided tape - horizontally at top & bottom & maybe between rows, but your layout might be a little tight for that. If you shortened your part a little bit below the bottom hole, you could maybe make room for that?
And I wouldn’t cut ALL of the holes, then ALL of the profiles. The most I would do is a row at a time… row of holes, then row of parts. Then if something goes wrong you have untouched material left to work with.