Small Engines (Lawn Mowers, etc.): K66 Tuff Torq Transmission Problems, open heart surgery, tuff torq

Question
Hello, I have a K66 transmission on my recently purchased  Simplicity garden tractor (1400hrs). The lady told me the drive belt was bad so it wouldn't climb hills. I found out after paying her $750 for the tractor and changing the belt that the transmission is not working properly. It drives fine forward and reverse on the flat but any incline forward or reverse doesn't happen. I've been told the K66 transmission is pretty much a "disposable" model and there is no use in spending any time performing "open heart surgery" on it. Best to replace with a new one. Problem is it's a lot cheaper to tear it apart and replace the innerds than to pay $1200 for a new one. Am I wasting time anad money opening up the transmission and trying to mess with the pumps etc.? Also, is the tractor worth spending the $750 plus repairs whether it's $500 in parts or $1200 in a tranny when it already has 1400 hrs on it?
I have submitted these concerns previously regarding my transmission problem and need a little clarification. The answer given seemed to be just change to oil out on my transmission or go to the TractorByNet link to view the parts needed to rebuild the basics on a K46 tranny (are they that similar?) I have been able to drain the oil out of the transmission and replaced it with approximately 1.5 quarts of synthetic 10W30 - the manual says it holds 2.5. I was told to run the transmission now to get the air out of it. Am I to believe that just by doing this I might be able to climb hills now? I have 6 kids and a one acre lawn that takes 4 hours to pushmow. Should I just ebay this thing and start over or is it really worth a shot? Tractor model is Simplicity Conquest 1694011. Transmission model is K66L Tuff Torq 1721952 (0004850). Thanks for your time!

Answer
I really don't have much experience with simplicity, so I may not be the best person to ask. What I would do is search on the Internet to find what this type of mower is going for to find out if it's worth it to you or not. I really don't know if you have the skills to work on the transmission or not, it's pretty technical.