Hey, not bad, especially from a piece of soft foam!
The 'key' (no pun intended) is in careful indexing. I have found that indexing to the center of the piece works for me. All I have to be careful about is making sure I set my machine centers 'exactly' in the center along the axis that will be flipped. Works pretty good for me.
Epilog 24TT 40w and Legend 36EXT 75w Laser Engravers, Roland SP-300V, BabyLoc PR600 Embroidery Machine, Panther 24" Vinyl Cutter, Mighty Presses (hat & T-Shirt), PRT48 Router