Amanda, Yes, you can rough cut with the 1/4" tool, and then finish with the 1/8. This is kinda complicated to accomplish and I'm sure others with more meshcam knowledge than me could help you out. However this is essentially the same process I'm using with Carbide Create.
What I was going to suggest was possibly trying another material, specifically Komatex expanded PVC, it's been a dream to work with for my business. Let me know if you need some help locating it. Usually calling your local plastics distributor is the best first step.