Presumably at 3.5 he can talk pretty well. Have you asked him how he feels about it? Is he embarrassed that he can't do it, or resentful that you want him to?
If he did several wees in various inconvenient places in quick succession, might he be trying to wind you up? Does he get lots of attention when he has an 'accident'? If he can wee on demand in the nursery, my guess is he knows what he's doing, although it might be worth getting the doctor to check his wee for infections (3 times in 2 mins is really a lot).
I did cold turkey with my ds at 2.25 and it worked pretty well, but three-year olds can be tricky anyway, and they're a lot more canny.
My bet would be nappies off, put him on the potty or loo every hour on the hour, and then bribery, and lots of it. Chocolate buttons, stickers, spiderman pants, whatever lights his fire. Star charts are a bit abstract for little ones. If he doesn't like you nagging him to go, put on one of those kitchen timers that rings a bell.
I'm not a fan of pull-ups as they're so absorbant they don't notice the wee. Have you considered plastic training pants with a folded-up terry inside if you want to minimise the mess? It'll be bulky and babyish, but that may be an incentive for him. If you need extra clothes stock up on cheap tracksuit bottoms in Oxfam or similar.
If you've taken a week off work for this, the stakes are pretty high. Chill. Lay in a stack of magazines and a bottle of wine and some chocolate. He won't go to secondary school in nappies. Truly, he won't.
Good luck!