Ok. Couple of comments:
Cut the long "outside" edges with a pair of heavy duty shears. There will be no need for cleaning up those edges as they will cut perfectly clean
Cut your inside shorter lines with your razor knife. Use straight edge for a "not-all-the-way-thru" cut, then your next cut will follow that score nicely
With a sharp blade you'll be thru cleanly in 1 score and no more than 2 passes
For the longer inside cuts, use one of your punches to get a starting access hole, then switch to the shears
For your post holes (made using your new punch set) I used a piece of 3/4" HDF (high density fiber board) as my base, it gives just enough to not deform the plastic before the punch cuts through. I tried a regular pine block and it was too soft. Note that the HDF will dull your punches but the ones you buy for this I view as limited use/disposable
I would not use a post to to "hold down" the protector ... it will warp and bow/buckle with playfield temp changes. Just let it free float
If there is a legitimate reason to affix the protector to the playfield, carefully center it so the edges are evenly spaced away from all playfield parts and affix it in ONE spot only AND, I would use a small piece of mylar not a post (which exerts compression on the protector surface) wax the spot first so you can experiment with placement and move it as needed)
Hope that helps and yes, clean any burrs (mostly from punches) using a small file
Also, don't get your template too tight to the posts. Do this ... grab a spare pinball. Roll it past your sling posts ... look how FAR the rolling edge of the ball is away from the post. Move in 1/4" from that line and your covered!
Don't worry too much about a perfect circle cut around pops. There is no punch big enough. Use a large punch to gain access, then cut the rest with shears.
BTW, really nice job on the template!