To cut the patterns in the panel, or just mount the Plexi?
For cutting the panel, you might check out local trade schools, high school metal shops, or perhaps a community college with a shop. A lot of 'em now have water jets or even laser cutters that they just need a simple drawing for and a scale (or too-scale to make it simple) for a pattern. Most cities or more industrial towns have businesses, and it's not as expensive as you might think. I had a panel laser cut with just a black and white pattern for $28. Took 4 days for them to get to it, but it was low on the priority list and I still think that was fast. It would have taken me 4 days to cut it out myself by hand. Dremels and small files rock, but sharp corners (like tips of sharp flame tips or scallops) or where the holes leave very little metal between cutouts (1/4" or so) and it can be a heartbreak when it turns to warped cooked bacon. It's worth a look around for someone to outsource it if it's any sort of complex design IMO. It's fun to say "I did that", but only when it looks spot on.
To mount the plexi, it might not be the "best" but I'd recommend just what you mentioned with just one big sheet. Not all panels are straight (or stay straight very long with a lot of material cut away), so what you may run into is a gap between the panel and the Plexi in spots. So whatever you use to seal the plexi to the panel with (clear liquid nails I guess), go ahead and put a thin coat all over the place. Not enough so that it squishes out and become visible, but just a skin coat. Maybe place a dab in the middle and then spread it thin with a little cheap foam brush.
Ive tried just painting the backside of the panel and then sticking the plexi to it and let it dry (redneck glue), but it wasn't a long term solution. A couple removals of the panel and it started to separate again. Maybe a year...