Ihaven't read all the comments, so I don't know if anyone has commented on using the Accuquilt Go. I sounds like your fabric is stretching. You can prevent that by putting a piece of clean white paper between the fabric and the mat. Accuquilt recommends that you do that - it won't hurt the dies.
I rarely use my rotary cutter anymore since I started using Accuquilt. I have most of the dies - and I love the strip cutters and the HST cutters. For HSTs, I put my Go next to my Pfaff, cut the fabric RST, pick up the HSTs and sew them in chains. It's almost magic!