Oiled stencil card or Cardboard is probably the best option for architectural models. The edges will be slightly burnt but should not be as bad as you describe. Air assist will help (if you have it).
Have you had your machine checked for alignment and also made sure the lens is clean and focus is correct? I actually get better results by adjusting focus to be slightly above the material. It increased the kerf slightly but reduces the power density.
You are correct in trying to keep the speed up but if you are unable to cut it in 1-pass then you will need to reduce speed or increase power.
Other materials that cut well and would work are basswood or thin ply.
There are lots of folks over at SMC doing architectural models, and very nice ones at that...