would abandon our agreement and run off into the subset with a new family. That fear is here again I think – she worries that if I get involved with this this new person I’ll be somehow less ‘committed’ to my daughter.
To a certain extent she’s right though - what has worked well for you both is now changing because you’re in a new relationship. You both agreed this was best for your DD but now (because it isn’t best for your GF) you’re changing the plan.
HOWEVER - that’s not to say you shouldn’t change it.
My ex stays in my house when I go away because it’s easier for the 3 DCs not I have to uproot their lives and live out of a ruck sack for days on end. He has a small place that doesn’t have a room for them so one ends up on the sofa, plus I have cats so he feeds them while I’m away too.
Your suggestion sounds very sensible to me, living closer, having somewhere which is also your DD’s home and making her welcome at both homes. Some parents have a house/flat which is the child’s home and then the parents take turns living there or in another joint property, so it’s them that do the upheaval rather than the child.
However that sounds fraught with issues if you don’t agree on fundamentals about tidiness, decorating etc but also if you want to move on with a new partner - which you both have every right to do.
People are territorial animals and staying somewhere where your partner’s ex lives and sleeps feels very odd indeed. I don’t even like staying at my DP’s house, as it’s full of stuff from his ex and makes me feel like she’s still there. If it was actually her house I would hate it, and would feel niggled by him being comfortable there among her things, with the smell of her around. 
1.Is it reasonable for my ex to expect me to honour my original commitment to always be there in her flat when she’s away (possibly for the next 4 years) – even though I’ve met someone new? no, things change, people move on. As long as you factor your DD into any decisions you make, you don’t have to stick to something that no longer works for you.
2.Is she right not to expect our daughter to have ‘two homes’ and not to have to move between our two places when she’s away (because it’s disruptive)? no, two HOMES is perfect - one home and one place you stay sometimes without any of your favourite things is a bit shit, but sadly the reality of many DCs, my own included. Two proper homes is ideal.
3.Is she putting a guilt trip on me about our daughter to prevent me from moving on? yes, sounds like that’s it.
4.If I do insist on changing things, am I being a bad person who has betrayed her by going back on our original agreement? no, your life has changed and you’re being considerate of your new GF as well as your DD - as well as your ex because you’re not expecting her to pick up any more parenting responsibility or to move herself or to stop going away for work etc You’re enabling her to continue in the same way, relying on you to facilitate her career, but doing it in a way that suits you too.
5.Are we really separated?. Maybe in her heart this is another cut to the tie that binds you and it’s making her difficult. She needs to accept that it’s over and work with you to find a solution that is good for you all. If she gets a new DP I’m sure he won’t want you in his place either.