I bought 60 yards of 1" by 1/32" double stick tape that works incredibly well for holding down parts(too well at times, using too much means I will lift my 50LB table top machine off the ground. That and snap thinner parts) for $26 on ebay. Perhaps using a little bit of the tape(like 6" of tape per square to start) with your current work holding system would work.
There is definitely a bit of movement when using tape, but so far I've noticed good finish quality. If you want to do tabs perhaps you could simply edit the gcode with NCPLOT and simply select a few points, then raise them up?

Anyways here is what double stick tape is helping me do.
Edges come out polished, and everything cuts out well with the tape.