Any 'slowness' in profiling is down to the signal path in use.
With a direct connection to Eizo, and using the internal TPG, the profiling will be faster than using resolve.
If it isn't, you have issues elsewhere... but impossible to guess where.
Also, there will no difference in 'stability' of ColourSpace when connected to any hardware/display.probe, or anything.
That just also shows you have something else 'wrong' in your setup somewhere - again, impossible to guess what that may be without actually being there.
Unfortunately, I can tell nothing from the screen grabs.
You will need to post the before profile, the LUT, and the verification profile.
However, the LUT Upload failure also shows you have issues somewhere outside of ColourSpace.
Probably a bad USB/Network connection?
Mob Boss at Light Illusion