I understand there may be another man but she swears there isn't
You've said this a few times in different ways, but it's still the same thing. She's denying an affair. Do you know that almost ALL cheaters deny affairs? Why bother asking her and why bother posting here that you ask and she denied? It's completely irrelevant what she says because cheaters LIE all the time.
and that she is so screwed up in the head at the moment that that is the last thing she would need in her life.
Don't make the mistake of expecting her to do things based on logic and common sense. You could say "she's so screwed up the last thing she needs is to break up with me" and you'd probably be right about that too.
When she left she told me to have faith and that she just needed some time. She said and I quote "I need to leave the marriage to save the marriage".
That's just BS to buy her time while she figures out that she has no intention of returning to you. She isn't coming back but she hasn't quite convinced herself of that. The more you chase her, the more you beg, plead, and remind her of how strong your love is for her and how much she means to you, the easier it will be for her to leave you. I know, you'd think she'd just come running back into your arms when she realizes she's about to lose this fantastic guy who will give her the world, unfortunately that thinking is flawed because it just doesn't work that way. She sees you more and more as this weak, even pathetic, clingy guy who is dependent on her for his very existence, who is crushed at the thought of losing her. Women want guys who are strong and independent and that is not the guy you are showing her when that is exactly what you need to be doing.
I totally thought there was another man but the only reason I stopped (or sometimes stop) thinking that is she put the place she bought in both our names. Anyone that is leaving her marriage for another man wouldn't sign a mortgage with the husband she was planning to leave for someone else.
I'm not saying there's another man, but if the ONLY reason you think there isn't is because she had you sign the mortgage, you better think again. She had you sign the mortgage because it puts you on the hook if she can't or won't pay it. If the mortgage is close to or possibly even greater than the value of the house, she didn't do you any favors, it's the other way around.