Can I re-write this sentence:
A good reason to have replaced the first "も" with "、" is to avoid the unfortunate, (but grammatically correct?), "もを" string of particles?
The correct sentence is:
This か is the question marker and forms an embedded question.
This should be straightforward because, in English, you should say "regardless of whether it's A or B", not "regardless of both A and B".
Of course you can also say it without 問わず at all:
But note that 国外でもを is ungrammatical because ～でも (="also in ～") is an adverbial phrase which never serves as an object marked with を.