I only have a little bit of familiarity with the actual anodizing process itself, but we do handle lots of masking issues, so I hope this is helpful.
I can't recommend which tape will be best for your particular application (though I'd start with lead foil), but in speaking with several anodizers who mask parts what is often helpful is a 24 hour wait. All masking tapes have a pressure sensitive adhesive. So, mask the parts, making sure to PRESS DOWN HARD on the tape (whether lead foil, aluminum foil or a polyester tape). What this does is activates the adhesive, which then "flows" into the molecular crevices and spaces over the next 24 hours (wait 48 hours if you can for best results).
By doing this, you will achieve much better "stop off" at the masking tape line because the tape will have had time to achieve best adhesion to the part. Hope that helps you to achieve better results.
Dave
Viadon, LLC - A cut above.
www.viadon.com