Should I get into contact with my ex?

I was with my ex-girlfriend for 1 year and 8 months (my first long term relationship) and we broke up this last September. She started hooking up with and then dating a guy that she had been getting coffee every once in a while with while we were dating around 4 weeks after we split. The split was mutual but was caused by my not being able to find a place to live after living at her apartment for nearly a year after doing a tour with a band (I was paying her rent and bills but since my credit is so bad I couldn't find a place of my own which I felt bad about). I initiated the breakup because I could feel that she wanted to distance herself from me and my plan was to make some space and then close in on our issues thus bringing us closer together and transitioning back into being in a healthy relationship. Within the 4 weeks before she committed to another guy, we were slowly working out our problems with one another and had civilized meet ups...mainly for me to pick stuff up from her place. I even wrote her a character letter to support her in her recent DUI case. Since then, maybe early November, I removed her from all of my social media because I couldn't stand to think about her being with another guy...no malicious or threatening messages from me by the way.

I should also mention that I've had a decent number of rebounds that have not made me feel any better...not to knock the character of these women. They were all great in their own ways but muscle memory prevails I guess.

Now its January, my career is starting to really take off but I can't sleep at night most nights because I can't stop thinking of them together. Her new guy is a burned out, out of shape, food truck worker with a tattoo of the joker on his arm so it's sort of frustrating to imagine her liking him considering she mentioned while I was with her that she'd never date someone like him (after my inquiring about what she thought about him after meeting with him for coffee). I'm considering reaching out to her...logic says that she's with him because she wants to be but my reasoning says "I can make you happier". I've been told that things are much less passionate and their honeymoon period has been more like "smoke weed and watch netflix" than when I was with her which was a firestorm of passion...picnics on mountains and traveling up the coast of California. I spent a great deal of money on her in the long run.

My friends have told me it's not worth it to include her back into my life (possibly out of protection) but my gut, stupid as it may be, won't allow me to let go at this moment. Should I continue pouring time into this? I know that no matter what, it will take time to stop thinking about her but that doesn't necessarily mean that I will act on thoughts alone.

Open to thoughts, thanks.