The "rules" to prove cohabitation are burdensome and if a judge rules for discovery on it, that means the court is willing to entertain that the relationship is more than that of simple room mates.
One would think that all that would be needed is the GF's bank statements to prove whether or not she is being financially supported by the OP, but people receiving alimony know the loopholes in cohabitation and do what they can to get around them. If the courts would make the requirements to prove cohabitation less burdensome, this type of stuff would most likely not happen. Of course, there must be some basis showing that they share chores, tasks, are recognized as a couple, etc. on top of the financials.
If a person chooses to accept alimony for any length of time, they have to be prepared to show proof that they continue to need the funds and accept that their privacy is going to be violated on an on-going basis. If OP chose to get involved with an alimony recipient, he should have been prepared to be called as a witness. The significant other is almost always called as a witness and typically has to provide proof that they are not financially assisting the alimony receiver. It's pretty much needed in order to prove cohabitation.
Frankly, in my opinion, if you hold yourself out to be a significant other of a person that you reside with for a period of 18 months or longer, it should automatically be ruled as cohabitation. Then a lot of this nonsense would stop. Of course, the attorneys would no longer profit as much from these cases, but it would at least be a realistic measure of the relationship. If there wasn't any underlying plan to commit to each other, folks would be less likely to live together if they realized that the alimony would be terminated after 18 months.
Sermon end.