I don't think this is a LTB thing tbh. Yes, the move is untenable without his help. But Retail managers are often cunts, telling you that you will get the sack if you don't do X,Y & Z.
If he is breaking down because of stress at work, I doubt you having a break is going to help him to get his act together.
IMO, putting the house move to one side for a moment, you NEED to talk to your OH. PROPERLY talk. You need to ask him why he was in tears on the phone. You need to find out what his work is telling him. You need to help him find a new job.
It's shit that your Ex is being more help than your OH with the house move, I get that, but it sounds to me like your OH is feeling pulled in all directions, feeling like he tries his hardest at work, tries his hardest at home, but he probably feels like he is doing a crap job at both.
What he needs to realise is that there are only EVER 24 hours in a day, some of which HAVE to be taken up with sleeping. If the majority of the others are spent at work, doing unpaid overtime as well as his usual hours, then his work-home balance is off.
It can be hard to see that when you are being pulled in all directions, and I've found retail to be particularly bad for it. --Thinks back to my 60hr/wk nightshifts when I was only meant to be doing 22.5hrs/wk...--
TALK to him. He can a) Pull a sickie using your D&V as an excuse. Though he may still be pressured into going into work... b) Tell his boss that he IS taking his planned time off, and he can't be sacked for that, and if he is, then he'll have no issue with going to a tribunal. c) Realise that this might actually be the thing you leave him over!
I can fully understand why you are wobbling at the thought of moving by yourself. My answer is DON'T DO IT.