That sounds really stressful, op,with the pressure of school in September. I have 4 children, and although I've never read the 'oh crap' method, I think I followed the basics of this, from what I've heard about it. It worked for 3 of mine, but not so well for 1 of them. At first I stressed about it, but then I forced myself to make the active decision not to stress, and I just did the following instead...
I just told him that we were throwing away the nappies and would be wearing pull-ups instead. I carried on with normal life, which like you, involved lots of time spent out the house. I just took him to the toilet every hour on the dot, the same at home or when we were out. If he managed to produce even a tiny wee, he'd get a choc button. If he'd wet/dirtied his pull-ups already, I just changed him with no fuss, and got him to sit on the potty/toilet for a minute. I didn't ask him to stay there long, just a couple of minutes, and he got the choc button if it was successful. I'd chat to him a lot about it all too. If he'd already done a wee in his pull-ups, I'd just lightly say 'oh that's a shame, you could have saved it for the potty and had a button', but I didn't get stressed about it. Eventually, bit by bit, he did more and more wees etc on the potty, and fewer and fewer wees in his pull-ups.
A few people disapproved of doing it this way, and said it would confuse him, and we should just lose the pull-ups, but honestly, it didn't confuse him. He learned that way, and it didn't take too long at all. It took the stress out of it all when the usual method hadn't really worked.
If your ds is withholding until he naps, don't worry. It shows he's capable of holding it in, which is a great sign of bladder control! Just stick the pull-up on him, and don't worry. You have three months. You could try what I suggest, and then re-evaluate in a month. He could be doing really well by then! Tell his nursery what you are doing, so they can stick to the same method.