I don't know that AP's have an "MO" to disrespect boundaries at all. I have a lot of AP and anxiously leaning FA friends and they respect my boundaries just fine if I explain them with warmth. Disrespectful and abusive people violate clearly stated boundaries, and they come in all attachment styles in my own experiences.
And we're not really discussing first dates on this forum usually. The partners of avoidants who come here are usually in long term relationships, and they are unaware of "the boundaries" because they get silence and deactivation rather than simple clear expression of boundaries. I find most of the forum members to be kind, good people who feel like they are in the dark because they don't get the communication they need, and their healthy attempts to resolve conflict are thwarted. They feel ostracized, abandoned, and afraid because of their partner's distances and breakups, confused by the cycling back, and would LOVE to hear them say exactly what to do to make things right. But they don't get that, because conflict resolution and clear communication promote closeness, not to mention equality. And maintaining distance , on their own terms, without compromise, is the avoidant's "MO".
Most people at some point unknowingly cross another person's boundaries. It does not make them disrespectful or abusive. If boundaries were that simple, this forum would not exist.
He is deactivating because we fought too much. I did overstep boundaries. It was a classic AP/DA cycle; Things were going well > I would start feeling insecure and need closeness/reassurance > he would pull away > I would freak out start a fight > he would pull away more > once things are calmer he would come back and things were ok again.
It's a lot more complicated than that but I'm simplifying for now.
He says he loves me and wants to work on things but he hates the fights so much, it's not want he wants. It's not what I want. I'm working on my own insecurities and need for external reassurance. Not for him but for myself. He needs to work on himself as well but for now, he has created distance between us by "breaking up" and now he feels the "threat" (my neediness) has eased he can come back (i.e. texting and calling me everyday) and right now we are the "everything is fine stage" but it's superficial, the issues are still there below the surface.
I refuse to feed into my negative thinking and AP behaviour. But my main question is, if I ask him to come visit me (explained in my original post) am I starting the cycle again?? Am I seeking closeness again?
It's hard to say as I don't know the timeframe or what has happened. It may be in an earlier thread I didn't read. There are probably other considerations with travel due to covid (I don't know how far he is from you). I don't think you ask him to visit, but ask him how he feels about travel in general right now .