What is your plan if things go well? You're 34, how important is having kids to you? Do you really think this could work?
If your gut is telling you you're not able to trust him again, even if you feel you 'should' give him another try, I'd walk away at this point. If you do think there's a decent chance of giving it a go but don't want to be in a terrible position if it doesn't work out, I'd think about a plan that could work in both scenarios.
Honestly, I think what would be 'fair' is if you bought a place to rent out, he rented out his flat, and you moved in somewhere together. Moving in together is a big step about figuring out how and if you will live together in the future: you moving in somewhere where he has already decided where the laundry detergent is kept and how everything is laid out is different and gives him more power. I'd be tempted to lay out a timeline: you both take out a one-year lease on a flat together, with a six month break clause, in the hope that if things are going well at the end of that year you will get engaged and either move back into his place on marriage, if it is nicer, or consider selling both properties and buy a joint one. I'm saying a year largely based on your ages and assuming you both have a desire to have children.
For that year, I wouldn't intermingle finances too much. If you were able to also buy a two bed, I would suggest renting just one room out, so you both have an easy way out: I think given he has been flakey in the past it might be worth renting a flat you could continue to rent for the year on your own if you needed to. I think having a plan - it may not be this one- that moves you both towards a shared goal is fair, but you absolutely have to have a trial period and you shouldn't be the one delaying your plans or being exposed to extra risk. If it works out and you marry, well that's both of you bringing a property asset into the marriage. If it doesn't, then you have a security net.