I agree with Jazz and wouldn't mind betting that it is variation in perspex thickness that is causing most of it. You can check this with a dial indicator once you have it held as well as possible in a custom vacuum fitting (I use PU model board mostly and a venturi vaccum generator on my compressor but a shop vac will do on non porous materials with light cuts)

Once you have determined how flat it isn't, you could probe a height map. There is a built in plugin with UCCNC called autoleveller which does this very simply and will compensate for tiny thickness variations if you have a good probe. It is one of many reasons why I use UCCNC. There may be plug-ins for Mach, Linux et al that do the same job.

Still a tricky one to engrave though. A bit of johnsons baby oil as a cutting fluid and running the job a couple of times may be in order. I have not tried a diamond drag knife so can't comment. I have just ordered one though! Cheers Boyan