John Deere 310D Reverser Issue

I have an issue with the reverser in my JD 310D. Here are the symptoms:

1. The machine doesn't go into gear right away when I switch the parking brake off.
2. When I switch the parking brake off, I have to flip the FNR lever back and forwards while at high RPMs a few times before the parking brake releases fully.
3. Once the machine is in gear and the parking brake fully released, the machine switches forward to reverse quickly and normally.
4. The parking brake never releases enough to disengage the warning beeper.
5. The machine does not have much power. It won't climb onto a trailer in 2nd gear.
6. The reverser is spitting fluid back from the reverser dipstick tube. The fluid that comes back up is foamy.

Does this sound like clutch packs, or something else? Is there another test I can try to make sure that this isn't a solenoid or an internal leakage before I tear the reverser out of the machine*? The diagnostic manual says that foamy fluid can be from a clogged suction screen. Could this be it? Is my next step checking for metal and fibers in the suction screen?

One point of interest is that the solenoid on the reverser is an aftermarket solenoid.

* How big of a job is this? Is there a cheaper rebuild kit than the one I can get from JD? I keep seeing references to a Case rebuild kit on this site, but I haven't seen any part numbers.

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John Deere 310D Reverser Issue