Thanks for all the wonderful tips. Using my good old Singer 401A, I was able to complete my first stippling efforts on a full-sized quilt to my satisfaction (not prize winning but not too shabby, either.)
Best tip was to tape an index card (with a hole for the needle) over the feed dogs. However, I finished the FMQ without the card, so maybe the card just helped me get used to manipulating the fabric.
I also think switching to a 100/16 needle and using Coats and Clark Dual Duty XP thread helped with breaking thread issues.