Koolfrog:
I think the advice already given by forum members is good; namely get professional prop shops/manufacturers into the picture.
That said, for what its worth, my boat's specs are not radically different from those you mention for yours. I've got a Yanmar 2QM20 (the transmission ratio is 2.14 to 1 -- attached is a photo of my engine name plate which is on the right side of the engine as you are looking from the pully side towards the aft direction), 36 ft, 13,500 lbs displacement. The Hunter factory prop which I had installed until very recently was a two blade 16" x 15p. The Yanmar tach would max out at ~2500 rpm vs the name plate 2600 rpm rating. So the 16x15 was a pretty good match to the boat and engine. Considering your 13" way different than a 16", it's good you are giving this some evaluation. Maybe there are some clearance issues with your boat that limits the boat to a smaller size prop?
I recently installed a Campbell Sailor prop which Steve Dion has already mentioned in this thread. I've had only a couple of outings on it, but initial impression is a noticeable improvement compared to the 2 blade. Boat seems to move forward nicely with less noise/vibration from the engine, with more speed at a given rpm (but this also might because of the newly painted bottom) ... And most particularly, my previous severe reverse prop walk is now reduced to something a lot more manageable. As said though, early days yet with this prop. I've only been in reverse a couple of times.