I have to ask a couple questions and have a couple comments as well..
What year is it and is it under warranty?
Do you have the WSM (workshop manual) for it?
If it's under warranty, I'd let the dealer diagnose it and fix it.
I'm not familiar with yours but both my M's (M9000's) are hydraulic shuttle and the modulating valve for the travelling pack is external to the transmission case and the lock up pressure is adjustable as it the lockup pressure for the PTO clutch pack. I'm assuming it's a true (no dry clutch) hydraulic shuttle with a damper plate in the bellhousing and no dry clutch. On my M9's the clutch pedal is linked to the modulating valve that controls the lockup pressure on the travelling pack and the shuttle lever controls the forward and reverse motion via a shift fork that works in sequence with the pack so when you shuttle, the pack disengages to allow the shift forks to slide the gear sets to achieve forward motion or reverse motion and then reengages the pack (pressure) to allow movement.
The WSM calls out the pressure but you need a fitting and pressure gauge to check it (which I have) and you can get from Motion Industries or Parker Hannifin.
I can look up the pressure for mine but it's probably not the same for yours.
I've never had an issue with either of mine but that isn't to say you don't. I still think the pump is deadheading.
While I don't advocate going to another forum for an answer, I would suggest posting your issue on Orange Tractor Talks. There are at least 2 very knowledgeable Kubota techs on that forum, White Tiger and Lugbolt. They can assist you.
Could be as simple as a linkage adjustment or pressure setting or as complex as a split (because either pack is only accessible by splitting the tractor. My one M has almost 5000 hours on it and the other is just above 2000 hours and I've never had any issues with mine other than upping the lock up pressure on the pto pack (which is why I have the gauge and fitting).
One thing about M's or at least the M9 series. They have weak PTO brakes so I run an external over running coupler on either of mine if the implement I'm using isn't equipped with it's own over running clutch. That was probably addressed as mine are both early 2000 models. I know Kubota has a refit but I never did it as mine are way out of warranty and the upgrade involves a split.