I didn't vote because your question is about your GF specifically.
So, you visit for a month each year. You enjoy that, she enjoys that too, or at least tolerates it for whatever benefit she derives from it. You didn't say what that benefit is for her, would it be correct to assume that it's financial support whether you are there or not? In any event, clearly one month per year is enough for her, and the "marriage" was an unofficial local ceremony to placate an older relative, with the added benefit of keeping you hooked.
This sounds a bit like a timeshare situation - - you only get to stay and enjoy the facilities during your brief alotted time, but in between you still have to pay ever-increasing monthly maintenance fees and occasional special assessments. And when you annualize it you discover that the accommodation is rather expensive for what you get, all for the illusion of ownership. And your unit most certainly does not sit around empty waiting for your next alloted time slot to come around.
On the other hand, if you haven't been sending financial support, then maybe it's not a bad arrangement - - you both have someone you know and like with whom to spend a month together each year. And you each have the other 11 months to do whatever you want enjoying your separate lives. That is not necessarily a bad arrangement as long as both people see it that way. Maybe you can strike a fair balance by coming around to her way of thinking, and check to make sure that your financial resources are allocated accordingly.
But if you want more than that, then it looks like that will have to come from another partner. And it's going to be very hard to find a partner who views the relationship as full-time and/or exclusive when you can only visit one month per year. So your current situation might be the best you can expect unless you find a local lady (local for you) or move.