I don't have much in the way of self-help advice, but I can give you my opinions.
BoringGuy is going to love this cliche. Ready, BG?
Everything happens for a reason.
Yep, I believe that.
Whether it's down to fate, or whether it's down to putting a positive spin on an event in order to get something from it, it doesn't matter. Every experience can teach you something, open a door, or put a change into motion.
Not all relationships stick. Relationships begin because of chemistry - literally, a chemical reaction. "They make me feel good".
Relationships end because of some sort of incompatibility. You have very clearly and honestly outlined a severe incompatibility between the two of you.
I would like to give you advice from your ex's perspective. With the exception of my GF, I am extremely non-committal with poly partners. As soon as they start to push, I pull back twice as far. The guilt causes me to hide away, avoid them, 'fob them off'.... which, of course, makes everything twenty times worse. She was very clear with you from the beginning and you were very clear with her.
Since it's only been 5 weeks, I really do think you're at great risk of continuing your pattern. I broke up with my last two secondary girlfriends because they needed more than I could offer. Instead of giving me space, they both continued to ask to chat online, on the phone or meet up, as friends. It was the last thing I wanted. If I'd had a 5 month relationship that made me feel claustrophobic, I'd probably need around the same amount of time before I could consider opening up the friendship arena in any serious way. I might actually need much longer. At minimum, I'd need about 3 months.
Of course, it's unbearably difficult for you too, because you're still left wanting more from her - just the way you were in your relationship. You're both still in your original pattern and that's to be expected, to be honest.
If it were me? I'd write an email. I'd save it, sleep on it, then read it again in the morning. This will be a cathartic exercise. Then, when you're happy with it, send it. I'd talk about how important she was to you, what you like about her as a person, what you understand and take responsibility for in terms of your breakup, how you regret that things got heated, but know that this happens. If it were me, I'd let her know that you never burn bridges and that your door is always open. I wouldn't even necessarily say "I'd love to be friends" - this might even be too much for her, if she's felt claustrophobic. Saying that a 'door is open' is far less intimidating. Once you've said everything openly and honestly, try to move on with your life and don't contact her again. If your friendship is valuable - if it's worthwhile enough, if it's going to be beneficial for both of you - you two will become friends again. But give it time. 5 weeks is not enough time to shake off the romantic attachment and previous cycle.