Removing the axles is actually easier compared to removing the transmission.

You say you can feel the slave cylinder pushing on the clutch fork, but can you actually see the clutch fork move? Take the rubber boot off of the front of the transmission that covers the clutch fork and have someone press the clutch. It should pivot like a see-saw.

I had a problem before where my slave cylinder gave out. After uninstalling it, it literally fell apart in my hands.