Hi S.,
Boy, am I glad to hear I'm not the only one who had this problem! My kids were suckers, too -- but they used pacifiers. I took a slightly controversial approach from the get-go -- I gave my kids pacifiers to keep the thumb at bay. Modern parenting being what it is, I knew I was allowed to remove a pacifier, but that it was strictly forbidden to remove a thumb. lol
My only idea is -- and this is a shot in the dark -- try to transition her attachment to a pacifier. Reinforce it with the nasty nail polish used to deter thumb-sucking. It may not work alone, but if she has a back-up source of comfort, perhaps it can deter her from the thumb. I know that seems backward, but once she attaches the sucking habit to an object rather than an appendage, you may have a shot at weaning her off the whole thing. The idea being that, at this point, she clearly can't go cold turkey.
After the habit of relying on the thumb is broken (weeks, probably?) then you can start easing back on the pacifier usage. I used various praise/experience related rewards to get my kids to use 'pluggy' ONLY at night. Then to use it ONLY to fall asleep (at which point I'd move it increasingly far away in the bed until they could go all night without it). Then I was able to have them give pluggy to the Pluggy Fairy who would deliver pluggies to all the new little babies who didn't have pluggies of their own. In return (as you've heard), she leaves a lovely 'big girl' sleep aid to take the place of pluggy. (I took my kids window shopping first. Seriously.)
The first few nights with nothing to suck on are tough, but that's the time to make sure you haven't lapsed on that foul nail polish -- just to keep the old habit from easily returning. Like I say, it's a shot in the dark, but it's the best my shriveled brain can come up with!
Good luck!
:-)