Already been said, but I'll say it again.
If you limit the Z one inch lower, you won't even have to worry about tool changes,
tools in the carousel won't fit under the spindle. Do a TC,1, there is maybe 3/8"
of clearance from the pull stud to the spindle face.
I'm assuming this is a ceiling clearance issue. If you don't want to or can't cut
a hole in the ceiling, this is what I would do.
Make a spacer and space the tool carousel down 1", then add a sheet metal strip
to the "umbrella" so the tools are still shielded (as well as they can be).
Then move your cold start position down 1". Should work fine, the only thing
you would have to worry about is you could over travel going down, but that
shouldn't be a big deal, I don't ever think I've hit the Z negative soft limit
in my life.
Another consideration on the 1". You may have to spin your resolver or encoder to
get the carousel to line up with your spindle, or you could just make your drop
a multiple of the lead screw pitch and not worry about it.
This would also be quick and easy to remove and return the machine to factory
configuration if you ever move to place with a respectable ceiling height, or
sell it.