Have you tried raising the acrylic above the cutting bed a little by putting maybe 1/4" pieces of wood under it? Maybe you are getting flash burn when the beam reflects off of the metal cutting grid sections.
Or, does the material come with the protective paper on it? Could you cut it first and remove the paper when done?
Maybe you could attach one of the drawings you use so that we could look at it also.
Regarding the corner power, if I'm cutting acrylic at 60 power, I set the corner power to 59. I don't know if that actually helps or not but that is how they cut acrylic in the demo video I received with my laser. They set the corner power one less than the main power setting.
Try raising it above the cutting grid a little, that might help.