There is not a band applied in 3rd. The intermediate band is applied in 2nd, and released for 3rd. Once this occurs the high/reverse clutch is engaged. It sounds like there is a delayed engagement of this clutch. The question is why this clutch is late in engaging. Could be a sticky valve, or could be a seal leak in that clutch pack. It applies in reverse, 3rd and 4th. if it was a leaky seal you probably would only notice it in reverse (which is notoriously slow anyway) and 3rd. Add to that the fact line pressure is boosted in reverse, which may mask any leak. You would not notice it in 4th as it would already have been applied in 3rd. This is a case where a pressure gauge would be a good diagnostic tool. If it is a sticky valve you could fix it in car. Leaky clutch, well... only likely to be fixed with a rebuild.
How does your fluid look ?
