I wouldn't do it, only a matter of time until something breaks. An LT was never designed for that kind of work.
Thank you for the mention!Update: success!
Flaken nailed it: the key is to ditch the turf tires and use higher traction ones. I got two of these:
Wound up just filling them with water and dismounting my mower deck (results in about the same total weight but more maneuverable). Now, I can stop pretty much wherever I need to on the slope when loaded, and can get back up the slope no problem with an empty bucket.