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The only thing that's different between engine off and engine on related to shifting is a spinning transmission input shaft. Based on that perspective, I have some ideas:
Misaligned shifter
Try a shifter alignment, it's relatively quick and free.
I'm not optimistic about this having a positive result since I'd imagine a misaligned shifter probably would cause notchy shifting with engine off.
Clutch isn't disengaging completely, which means the input shaft isn't slowing down appropriately
The transmission's synchros have the job of braking the input shaft, but it's hard for them to do this if the input shaft is being actively driven while the clutch pedal is depressed
Could be related to clutch fluid, but could also be related to clutch master and/or slave cylinders
Could also be related to clutch/pressure plate itself
Transmission isn't adequately lubricated, synchros might need more or better fluid
Drain & refill trans fluid. Many people have reported improved shifting characteristics from a fluid change.
Transmission has worn synchros
Not as likely if the behavior you're experiencing occurs in most/all gears
My suggestion would be to drop the clutch inspection cover to get a better look at the clutch's operation. Gotta drop the midpipes to access it.
The only thing that's different between engine off and engine on related to shifting is a spinning transmission input shaft. .
....and the steady decrease in fluid viscosity as trans temperature increases. As you have already suggested, a fluid change will remove this variable.
....and the steady decrease in fluid viscosity as trans temperature increases. As you have already suggested, a fluid change will remove this variable.
For better or worse, I made the assumption that shifting is notchy as soon as the engine is fired up and trans fluid is still cold.