I think Code54 is on the money. Here are some more things I tried, then I'll tell you what the Kubota mechanic said:
After tinkering a bit and talking a lot, my best and most logical guess is that the rear diff lock is sticking. The pedal itself does not stick, and it actually appears to function normally -- ie I have to depress and hold the pedal while moving slowly to fully engage it.
Here's the really confusing part. I jacked it up today, disconnected the pedal linkage and manually worked the lever. With the tranny lever in neutral, I worked each tire forward and back. As I spun one tire forward, the other tire spun in the reverse direction, and vice versa. I then manually engaged the diff lock lever and both tires spun in the same direction together, as if the rear diff lock was engaged.
I then started the tractor - while jacked up - and worked the HST pedal forward and reverse. I was able to hold the HST pedal side tire for several seconds while the other side axle kept spinning. The limited slip action of the diff seemed to then kick in and the tire I was holding spun out of my hands. I then tried it in reverse, and I was able to hold the same tire indefinitely while the other side kept spinning. I then manually engaged the diff lock lever and both wheels spun together in the same direction and I was not able to hold the tire at all -- seemed like the diff lock was working.
Thinking everything was okay, I tried cutting the grass again and same old thing. Inside tire tearing up grass, even going extremely slowly. I drove up to a log pile in low range and both tires spun together, like the rear diff was locked...but i didn't step on the pedal.
--So I stopped by the dealer and explained what I did above. He said, like Code54 theorized, something to do with the fork is likely bent internally. That defect is probably causing the rear diff lock to remain partially engaged. He said it is 8 hours of labor just to pull the rear end out, which is what they have to do. I'm thinking about tinkering some more with the lever and then just pulling it out myself. What a nightmare. The worst part is that the only symptom (right now) is the power to both tires. They basically cautioned me I could tear the rear end up. Ugh.