Problems with LX277AWS transmission

Hi all, I have a 2000 JD LX277AWS (All wheel steer) with a hydrostatic transmission that for the past 2 or 3 years, when I press the pedal to go in reverse, it really labors to move, especially when trying to reverse up in incline. Now it's getting to the point where the lawn tractor will not move in reverse on an incline. When I press the pedal to go forward, I now am experiencing a bog down especially up hill but not nearly as bad as when trying to go backwards. I got this mower from my brother who had it for 5 years before giving it to me. He claims to have done all of the maintenance but I don't know about the transmission fluid and filter. Perhaps changing the oil and filter in the transmission should be my course of action but other than the possibility of the old oil and dirty filter, what else can go bad in this type of transmission? I have no experience with hydrostatics, just geared transmissions. Oh, BTW, the main drive belt is new. I had to replace it 2 weeks ago when the old one snapped. I was really hoping that the bad belt was the culprit, but the problems remains; it bogs and labors when trying to use it. Thanks in advance for your help. Roger