From my distance (MA) nothing is certain - but if you've noticed the HST getting worse over time and the dealer has already tried external adjustments (not much is possible) replacing the HST may be what's needed.
This HST is the next generation after the one in my L48. It's redesigned for the L30 tractor models but the operating principles are the same. They have very high-precision internals and rely on perfectly clean fluid. They usually last a VERY long time without trouble. But the smallest metal fragments can ruin the mirror-finish surfaces on the slippers, swash plate, valve block etc. So when they stop functioning the damage is often extensive and a new unit is the only practical solution.
The part number for the unit is TD060-59994 - Internet search returns price numbers like $8,800. If a dealer installs it, add another few $k for labor (open-station or cab?) plus normal replacement parts like clutch, shaft seals, filters fluids etc. The repair may come close to what the tractor's market value would be (if fixed).
When the prior owner of my L48 decided to sell it rather than pay a huge repair bill, one factor was the extra labor caused by the machine's subframe. Yours doesn't have that but the HST cost is now 180% of what the prior model HST was then. I bought my L48 knowing it needed an HST job - it was only slow in reverse - so I took a chance that most of the high dollar assemblies inside were still good - they were. (and it's still going fine)
If you are mechanically handy there are some other ways to go. Used HST's are extremely rare and hard to find. But if one can be located it should be well-below the new price. If we could come up with a used one I'd bring over a 12-pack and we could give it a go? -pretty far away - maybe texting would work better! Talk more soon - take care, Dick B