The salary would be about 30% more than his current one.
Will this be enough to completely cover the costs of supporting a second household? Because I'd sure as hell be unhappy if I found out I'd have to change lower my standard of living to support his 'new' life!!! And what about transportation? Is he going to expect to take off with the family car or buy a new one in his new location? Will that 30% also cover airfare back and forth for him, you, & DDs for visits? Because if this happens, I'd sure as hell make my presence known in this 'new life' by visiting him (and expecting to socialize with his new friends) and not just having him fly home!
Honestly, there are sooo many unanswered questions about his 'plans'. It's like he just wants to trot off to this new life with no forethought about the practicalities.
He is going to apply but keep consulting and checking in at every step
What's that supposed to accomplish? Does he think that if he 'consults' and 'checks in' with you that will pacify you make you suddenly love the idea? Phffft! It's just paying you lip service to make you feel you have some say in this. Do you seriously think he's going to take all the steps and interviews to get this job and then suddenly say at the final offer "No, sorry, can't do that. The wife doesn't like it". Hell, no he's not going to do that!
When my DH took the out of town job, he'd been out of work for close to 2 years due to a work injury & then retraining. He plastered our area with applications once he had his new qualification but there were just no openings. We were barely making it on my salary and a bit of help from my parents. It was pretty much a 'no brainer' that he'd have to take any job offered and we'd make it work but he'd continue to pursue jobs closer to home. We ended up moving to where his job was after 2.5 years of him only home weekends. But that's not your situation. Your DH could look for a better job closer to home.
I'm not saying that a 'commuter marriage' can't work. It can, but ALL parties have to be 100% in.