I realize the short answer may be \'no,\' but perhaps this is worth asking again.
If I am witting a Kivy app with a couple thousand of lines - then would it be possible
Yes it is! You can import .kv
files inside files just like normal python files by starting with:
#:include otherfile.kv
If you want the file to unload and reload first you can force the import typing
#:include force otherfile.kv
instead.
All this as written in the Kivy Language Documentation which is full of useful clarifications.