That sounds just like the filter plugging. A transmission filter basically plugs for 2 reasons.
1: Something is failing rapidly internal, which creates excessive metal and/or clutch material to plug the filter. You can renew the filter but the glory will be short lived. Usually you drive a 1/2 mile then it plugs, then you let sit awhile, then you go another 1/2 mile, plugs and so on.
2: Normal wear and tear with many years and thousands/millions of miles on it and the filter has never been changed. Hopefully this would be your case
Drop the pan to inspect condition and if its at a "reputable" transmission shop they "should", know what is, for the most part, going on.