Interesting...
Just read my Kubota MX6000 - Hydro manual again and there's no mention of normal operation REQUIRING coming to a stop to shift in or out of 4WD.
It does mention coming to a stop and try going Fwd or Rev, else try turning the steering wheel if difficulty with 4WD shifting.
I may have similar lead. I would have called it "windup or tension" on the MX. Most of the time, from habit now, I stop the tractor and rock it, inching it back, then inching it forward to disengage 4WD.
It easily drops INTO 4WD without issue while underway at low speed.
Mr. Lou, this thread is interesting. With 1200 hours, my tires are wearing, but not EOL yet. I normally mow in 2WD, but with 12 acres to mow tomorrow, I'll have time to play with different front tire pressures and effect on 4WD shifting to see if I can find a sweet spot.
Until this thread, and Mr. Gordon's comment, I thought the need to "stop and rock" to disengage 4WD was "normal"!