think he is undeterred and overtired... is that possible?
Not entirely sure what you mean here ?
But if he's touchy then I would go slowly and carefully with extending A times, as touchies tend to be very sensitive to OT as well as OS. By all means extend by 15 mins and give him 3 days or so to catch up and see how he's doing. But I would definitely not make a big jump all of a sudden. And you don't want to get into a cycle of OT NWs either (yuck).
My touchy LO would not nap anywhere other than in his cot either so I can't really offer any tips on that sorry! Bear in mind that he's 10.5 months now, he is likely to transition to one big nap in the coming months. Again, I would caution against rushing him even if it feels like it's the solution to your difficulties.
I wonder if his middle of the day A is too long at 4.5 hours, and the following nap too short? His first A is only 3 hours so there's a bit of an unbalance there..? At his age, I would be tempted to push the AM nap a bit later, cut it shorter (say to 1.5 hrs) and bring his PM nap earlier too. TBH, with my two, we always did the AM nap as the shortest so that the (early) PM nap could be longer and more restorative getting towards BT, but that might not suit you. Perhaps you could say what your ideal day would look like? You haven't mentioned the afternoon school-run?
Don't worry too much about nursery. If it's only two days a week, he will adjust and you will be able to balance out and catch up if need be on days off.