Sounds like you've got this under control but I'll offer my experiences for other users.
We've got a competing brand commercial mower approximately equivalent to Kubota. My bet is most all the top-line brands use the same basic components. I don't think Kubota or anybody else--as regards mower hydraulic systems--manufactures their own hydraulc drive motors from a raw chunk of steel: they use some supplier, e.g., Eaton or similar--even though the part may have a Kubota part number.
Anywhich, I had the same problem refilling the hydraulic fluid (slow, bubbling, burping air) into the drive system. I finally looked closely at the schematic parts breakdown and discovered an Allen-wrench head plug at the very top of the drive motor, one on each side.
The plug doesn't seem to serve any purpose, didn't have any springs or balls shown under it, and was lock-tighted solidly in place. A tiny bit of heat from a torch warmed an Allen wrench and liquified the threadlocker. Out she came.
Now I've got a vent. When refilling fill from the bottom after removing the top formerly threadlocked vent. When fluid reaches the vent, reinstall both plugs.
Later I asked the Senior Tech at the dealer and he admitted that's how they do it--refill fluid--because it's faster, but the procedure isn't shown in the Owner's Manual nor in the Shop Manual. The Tech said he's been told by the Mfr Field Rep that the plug is indeed a vent but used only at the factory to fill the system "for speed during assembly", then threadlocked and forgotten about.
So three things: (1) check the equipment itself and (2) check the parts schematic for 'hidden' features, and (3) talk with your local knowledgeable service department.
Please post other experiences along this line so we may all learn.