It sounds like the typical "well used" hydrostatic drive transmission in dire need of a fluid change. If you did not change the fluid in either of the trans units you now own you should expect that both contain oil that is degraded beyond a useful condition.
At least you know how (I hope) to remove the transaxle assembly because that may be the best way to drain out the old oil.

What type and how much fluid should be used?

Your transaxle is supposed to be a Hydro Gear brand, model # 319-0650.
According to the Hydro Gear PDF parts list (get your copy by clicking the link below) your transaxle requires 81 ounces of 20 W 50 motor oil. I recommend synthetic (it's great in heat).
Now, think real hard............do you remember seeing (in print) somewhere that your transaxle is a 319-0650? :^)

Here is a link that might be useful: 319-0650

Thanks again mownie. Since it is late, I will check the number on the transaxle tomorrow, but I think the number you posted is correct.

The transaxle is indeed a Hydro Gear Model 319-0650 as referenced by the sticker plate on the unit(s). Thanks for the advise and the link. I will start the dissembly tomorrow. Do you think it is wise to change-out the pulleys and drive belt while I have it taken apart? The transaxle pulley shows some wear inside the "v". I can't really see the crankshaft pulley without taking it apart. I am tired of working on this thing and want this to be the last time I have to put it on the rack.

If the belt looks good (not cracking or glazed) and the bottom of the vee on the belt does not reach the bottom of the pulley vee, no reason to change the belt or pulley (so long as the pulley is not loose on the input shaft).
Are you intending to change the oil?

The oil will definitely be changed to a synthetic 20 w 50. The belt does show signs of bottoming out in the pulley so I am going to change them (the belt and pulleys) out. Previously when I was first working on this tractor, I saw a listing on ebay for a hydrostatic "tune-up" kit which stated that wear to the pulleys were the main problem with poor performance in hydrostatic drives, but I can't seem to find the listing anymore. The kit consisted of the belt and both pulleys and was somewhat cheaper than buying the parts individually. If anyone knows where I can find this, I would really appreciate being told.

HALLELUIA, HALLELUIA!!! The Angels are singing and this old man is smiling! Many thanks to you mownie. I changed the fluid in the transaxle and replaced the crankshaft pulley, the ground drive belt and the transaxle pulley and the tractor now pulls like a champ. I did not use a fully synthetic fluid ($8.49 per quart is too rich for my blood) but did use a synthetic blend. Auto Zone had a special for 5 quarts and you get a free oil filter. I also changed the fluid in my other hydrostatic drive mower. I think the real culprit was the crankshaft pulley. The interior of the pulley was worn so round that the belt was only touching on the innermost surface. Thanks again mownie you are a true expert. I hope I don't ever have to go through this again. I think I could change-out a transaxle in my sleep!

Well, I'm just a dumazz mechanic. But I do enjoy watch a happy person turn cartwheeels!

You're #1 in my book! THANK YOU.

Ocmoses

The joy of the moment is clouding your judgment. Thanks.
:^)