Ryan
From looking at the WSM I see the operating pressure for the IC shuttle is controlled by the pto clutch hydraulics.
Does your pto engage properly or is it slow to lock up?
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I have not personally worked on this model. Checking pressures and adjusting them if out of spec does not look too difficult.
Digging into the transmission internals does not look like a place to go if you do not have Kubota training.
The M7040 series with hydraulic shuttle does not have a clutch in the traditional sense of the word with a disc being pressed against the engine flywheel. Instead there is a coupling device that connects the flywheel to the transmission shaft and the clutch pedal is just using the shuttle clutch packs when you depress the clutch pedal.
The M8580 seems to still use a traveling clutch in addition to the shuttle clutches. Double check that you have adequate free play in your clutch pedal and that the symptoms you are experiencing are not from a worn out clutch.
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Dave