Dan Savage uses the phrase "price of admission" to talk about the things that wouldn't be our preference but that we're willing to accept to be with the person/people we want to be with. A temporary suspension of contact with other women seems like a perfectly reasonable price of admission to a new relationship to me. If it was intended to be a permanent thing, especially since she can't/won't commit to more involvement in your life, I'd see that as problematic. But many people need special rules while they're adjusting to a new poly situation.
It's "fair" to ask for whatever you want or need. But if you don't want/need casual sex with strange women right now, why *not* concede that if it's what she needs? I think your choices make perfect sense, as long a she's being a thoughtful partner, genuinely working to give you the freedoms you want, and being there for you to the extent that she can.
It's true that a close friendship with sex that evolves into a relationship really doesn't look much different at first. But in time, for me at least, I found that making the distinction came to make a big difference.
The major players. Me, 30ish bi female. Gia, girlfriend of 4+ years. Clay, boyfriend/dom. Davis, ex/friend/"it's complicated." Eddie, roommate & fwb.
The supporting cast. Eric, Gia's husband. Bee, Gia and Eric's toddler. Dexter, Gia's lover. Helen, Eric's lover. Izzy and Nikki, Clay's partners. Liam, Eddie's husband.