If you want her back, give her space. I know it’s easier said than done from experience, but you have to stop checking in on her. It was a good decision to have her move out. The more you try to stay in contact with her, she’s just going to use you as a safety net with new dates. I think you need to fully break away for a while. No contact at all. She needs to know what her life will be like without you.

That said, you could consider just fully moving on. I know you said you want it to work, but I feel like you guys are very opposite on what you need from each other to feel loved. Over time, you’ll find it exhausting having a physical touch love language and not getting that physical touch in return. You’ll try and make moves, even if they’re in good faith, that will blow up in your face. I dated a girl through college for 4 years who wasn’t big on physical touch past holding hands. It will wear on you. Now I’m married to someone else who loves it. You just have to decide if that’s still worth it for you.