It's true that some children who suck their thumb may not end up appearing to have dental/skeletal problems, but I've seen many who have needed major orthodontic and/or surgical intervention to correct problems that were caused by long-term, agressive thumbsucking. Here is a case example of what can happen when thumbsucking is not stopped before the permanent teeth start coming in (keep in mind the first picture is of the child's natural bite with the back teeth closed together):
http://www.cumc.columbia.edu/news/dental/cdr97/mehrnia.html
M., my heart goes out to you and your daughter! I know that thumbsucking can be a very hard habit for a little one to break! As a dentist, I wouldn't recommend waiting until she's ready to stop on her own since she's already almost six years-old. However, I would certainly try various positive reinforcement methods (like the chart you mentioned)...you may get lucky and find one that will work with your daughter. Don't get discouraged because she got upset when you showed her the reward/goal chart...try, try again! I think it will be easier to make very small goals---just as you said---such as trying to break the habit first during T.V. viewing, then maybe move onto travel time, then save the night time for the last goal.
Here are two informative sites you may find helpful:
http://www.ada.org/public/topics/thumbsucking.asp
http://www.aapd.org/media/pressreleases/ace-99.asp
I wish you and your daughter the best of luck!!!