Nomen Nescio writes:

By already being in a climb at "one altitude" and maintaining it through
"another".

At some point your vertical speed must change, and then your net acceleration
will change as well.

Wrong!
It's not!

It is constant for all practical purposes.

If one G is defined as 32.2 ft/sec/sec, it can be done. I'll leave it to
you to figure out how.

It cannot be done, and you cannot demonstrate otherwise.