I dealt with this recently on my custom build. I used a combination of a rivet clamp from Marco (which worked well, but only near edges where the tool could fit) and the hammer and punch you mentioned. This method is okay with some preparation and self-control. Place the plastics upside-down (so the round rivet heads face downwards) on top of something very hard and rigid; mostly I used the anvil surface of a benchtop vise. MAKE SURE to put down something protective, such as a rag, so the plastic doesn't get scratched by that surface. Place your center punch on the backside of each rivet, and give it a few taps with the hammer. You will be able to see the rivet being flared out as it happens (assuming you are using similar sized rivets/punch as I did), so vary your hammering strength so that you fill the gap between plastic and rivet, but don't overdo it or you will squeeze the plastic and make spiderweb cracks.

In contrast, pop rivets - the type with a hole after assembly - require a lot of force to apply, and are very likely to damage the plastic in the process.

You may want to wait for others to chime in about this before proceeding, but this method worked very well for me.

I sure wasn't! I finally settled on the hybrid design because it looks at least half modern, definitely a bit industrial, doesn't require ramp protectors but does let you see through it, etc. Definitely use rivets instead of screws for mounting, or else you'll have a lot of screws falling out.