As far as I am aware, the reason that some transmissions start to slip after having a prolonged transmission fluid service/change, is because the old fluid degraded, the clutches wore out because of it, and now the clutch friction material is floating around in the fluid instead. Changing all of the fluid could cause those clutches to "lose traction" and start to slip. Very few places now use power flushes, it's usually a drain and fill/cooler flush.
My personal opinion, I'd do a cooler flush if you can, plus transmission filter/gasket change. Reason being, a drain and fill is 3-4 qt. and the transmission holds roughly 14 qts. It's going to take a lot of drain and fill changes to properly renew the fluid, during which time you're subjecting your transmission to mostly old fluid and towing a boat. Not recommended, (my opinion).
Cooler flushes are easy and take 2-3 hours I'd say if you're taking your time and the cooler is easy to reach. Lots of writes I'm sure online already.
Anyway, if it's any consolation, I have 190k on my transmission (last change I think was was at 100-110k) and I did a full cooler flush on mine and there's no slipping. Fluid came out horrible dark red/black, and I hate to think of leaving it in there. It's very noticeable how much smoother it is and I'm sure my gearbox is happier now. Total cost was $220, DIY labor.