Going by what (limited) experience I have with these motors - it seems there are a number of differences that might help differentiate the model years.
The earliest 310 I have is #19, it has a heavy 4-hole flywheel and no ID plate on the transom bracket, the number is stamped right into the aluminum bracket like 49morphew's motor. This motor had the short tiller on it and no ON/OFF switch on the tiller handle bracket.
The newer 310 is in the 800 s/n range (no "P" suffix) and has a three-hole flywheel, longer tiller (you could get them with one or the other on all models) but has the added on-off switch in the transom bracket. Ditto for a model 310 in the 700 range that I sold a few years ago, but it didn't have the "P" suffix on the ID plate.
It seems if there's no ID plate on the transom bracket, they stamped the number in where the plate ought to be and that's all.
If they have an ID plate, they stamped the plate plus another location that is usually low on the starboard side of the engine block. Coupled with the change in flywheel styles, and addition of the ignition toggle switch, motors with these features might be post 1930 models, since I believe that its possible that at least some of the 1930 models didn't come with an ID plate. However, as much as I'd like to, I can't suggest a point at which Evinrude transitioned into using the plate as well as secondary s/n location.
Unfortunately, none of that answers the "P" designation question, but at this point the only other thing I have to offer is that I have no record nor recollection of seeing any of the 1930 four-hole flywheel Sr Speedsters with the "P" added to the serial number.
Hope this helps.