The desire she has to see other men shows that something else is going on and that she is not ready for a full commitment with you.
Even if you were moving next to her straight away, this would still not solve the issue.
The emotional distance she decides to take now would still be there.
If that's what she wants, consider yourself 100% free.
Soon, she might start to date other men as she says she will.
You need to be ready for that and have already your life back when this happens.
Yes! Distance and lack of commitment on her side are deal breakers.
The only way you would solve this is if either you or her change your minds.
Your two visions simply don't match right now.
Should you go for an open relationship?
Honestly, I think that only 10% of couples are actually ready to make an open relationship work.
It can be super challenging for one or both partners.
If your mind is already set anyway on wanting commitment, I would say: No, you don't have to.
Now, if you do want to give it a try, you can say something like:
"Well, I thought about it and I want to give it a try. Yes, let's have an open relationship for a month and see how it feels. "
"We both agree that we can date other people. I might go on dates myself as well. Are we clear on that? I am not saying that it will work, but let's give it a try and check it out again one month from now..."
By the way, if you want to try an open relationship, there is much more you must know.
I would advise you to sign up for a couple of coaching sessions.
http://vitalcoaching.com/coaching.htm
I would need to talk with you live because it's a big chunk with many potential challenges.
What about convincing her to change her mind?
With the distance and the fact that you won't see each other much, that will be very difficult. You already tried. Her answer was "No thanks".
As you noticed, pressure, demands or trying to reason her do not help.
A commitment needs to happen because she wants it with all her being.
Right now she already pulled back emotionally.