Not necessarily; that it runs normally without the long strain of that particular hill means you may have caught it in time for some preventative maintenance. Mine went out quickly, so you have a different scenario.
Frankly, in my experience your biggest problem will be finding a shop that will attempt to repair it without rebuilding it. I understand the thinking, because transmission repair is extremely labor intensive, and were I a shop owner, I would be concerned about the possibility of an ineffective repair or other problems showing up later and the customer's quite reasonable expectation of warranty protection.
However, I have heard Aamco Transmission radio ads that specifically stated that many repairs they perform don't involve complete rebuilds.
I'd start Googling local shops looking for customer reviews, then call the most promising ones. In no other form of vehicle repair is the term "caveat emptor" more applicable than transmission repair, so do your homework thoroughly.