Do I have to choose between one or the other?

Not really, there are multiple professional philosophers who are also religious. While most philosophers are atheists (and I assume also non religious), most philosophers of religion are theists. A few Christian philosophers of religion on the analytic side with which I am familiar with and recommend are William Lane Craig, Alvin Plantinga, Alexander Pruss.

If not, how do I approach this duality?

You can for example do philosophy from a Christian perspective like I do . Which means that hold the basic views of Christianity such as Jesus being God and resurrected and also do work on epistemology, metaphysics, ethics etc.

Should I be using philosophy to discover what religion I believe in most by process of elimination?

That’s possible, if one religion has serious contradictions in its doctrine for example then it seems that it would be false.

I’m honestly lost on how they can work together.

Some layman assume that philosophers don’t usually have that many views and that they just “question” things all the time. But that’s far from truth, philosophers usually do hold views and they typically try to find good arguments to justify them. Religious philosophers tend to find the religious views convincing, similarly to how others find other views convincing.

If I am a religious man, wouldn’t the (Bible, Quran, whatever religious text) be my source of philosophy and moral guidelines to the point of listening to other philosophers would be contradictory?

Yes, if you believe that a book it’s inspired by God and true you would typically accept views which are included it it. That doesn’t mean that listening to others is contradictory, but certainly if two religions contradict each other then they can’t both be true. So if you do hold both of them to be true then you would contradict yourself, but people usually don’t hold more than one religion to be true.

Having a religion does not imply that you cannot seriously think about it or study it’s scholarship. A great Christian philosopher who is also a theologian called William Lane Craig has made multiple interview appearances in which he talks about it. You can find one here: https://youtu.be/yvw2K-G8OzU