Hmm- I have several thoughts here. If you say you are due for fluid service soon, changing the tranny filter without changing the fluid for troubleshooting wont hurt anything. Just make sure you replace it again with new fluid when you are ready to do the service. Its possible the filter is full to point where its pluggin up.
The other thought is you didnt say whats the rpm you have it at going up the hill. were you able to make it up the hill before with same tractor ? I hope you are always using low gear for hills with rpms higher then 2200.
How is the engine running going up hills ? lugging ?
When going up the hills, its possible the releif valve is kicking in early which indicate a possible weak spring. You could replace the spring, but then you might need to add shims to bring up to specs, so if you don't have the test gauge for hydraulic, it might be better to take it to the dealer to check the pressure and replace spring and add shims as needed.
However if you disregard my thoughts above and focus on the part where diff lock helps, are you going up the hill at a angle, is it possible the path is worn out causing one side to be soft and other hard causing the differentail to kick in? I can't tell from your posts.
