Hi Andy's Mum!
By reading your post i would place a bet on teething, symptoms and age and being a textbook baby i can guarantee it's about molars. They are HUGE routine breakers and can turn the angel babies into bears without aparent reason. 13 months is the mark for bad nights if you happen to read some of the posts around here, many moms are struggling with kids that age. I was one of them and tried EVERYTHING (wake to sleep, etc) and nothing seemed to work until i gave a mix of paracetamol and ibuprofen TOGETHER. And yes, there were no lumps/white bumps for a while (I'm talking about 3 weeks). Average time for molars to pop up are 2 months, and the ped explained me that textbook babies are OK during the day but it's when they're relaxed (that is, sleeping deeply as in night sleep) that they are bothered by the pain. Try that combo, cause paracetamol is a very mild pain killer and apparently molar pain is LOTS bigger than a simple teething pain. At least, that's been the case around here quite a lot.
I don't think his napping is affecting his night sleep. He seems to nap quite fine and being on this good routine he is, it sounds perfectly logical to me that he wants to make up for lost sleep during the day.
The vomiting might have been caused by the fingers in the mouth. My ds uses to scratch so hard that he manages to put his whole fist in his mouth, of course causing a gagging reflex, hence the vomit. Some oraljel before bed might also do the trick with that.
We got so badly on a period that i even tried an homeopatic remedy along with all the meds and that also seemed to help for a few nights (it was not magic but it got better). We used to have that inconsolable crying you're describing that lasted for 2 hours and he continued to wake during the teething process but he'd be easily calmed with pat/shs and some reassurance and some wi/wo not longer than 10 mins once the meds and all the other remedies were being used.
Also, i would stop offering the breast. It might seem to calm him but that's just because of the chewing he gets to do, so he might seem comforted and then get used to it and then you will have another thing to get rid off. If he's desperate to chew on something, offer a blankie or a paci, but i think the chewing anxiety might be solved with a teething gel.
HTH and keep us posted so we can think of anything else to help you out Good luck!