Although I don't have davits I can say that a 3.10 meter dingy fits nicely on the aft coach-roof assuming you cover the shower-hatch.. My guess is that 3.40 meter would be very tight.
Typically we keep it on the aft coach-roof and also deflated. Ours has a polyester bottom (a very simple PVC model from Plastimo). In the marina where we typically are we move the dingy a bit aft to clear the shower hatch. It then interferes with the mizzen-traveller, but in the marina there is obviously now issue with that. It also limits the opening of the aft locker in that position, we need to secure it to stay open.
PVC/Hypalon. From what I saw the price-difference is not that big. but is has been a while since I looked. If you want to keep the dingy for several years in the tropics and use it intensively, there is only the choice for Hypalon, unless you make/buy tube covers. Here in the Caribbean you see almost exclusively Hypalon apart from a poor guy on an Amel 54 ;-)