I helped a guy sometime ago with a seadrive and fixed his problem. You say you have to run it at 4400 to get a 20 mph speed. What throttle setting is this? Is this all the way forward, aka wide open throttle? If not my answer below is incorrect. Outboards are not like cars. They are built to run at wide open throttle all day. As a matter of fact my experience indicates that 2 strokers like it that way. If you are trying to "soft pedal" the throttle you are on the wrong road.
Also as spike said dia changes with pitch change but for a given size gearbox...the contents of the casting in front of the prop there is a given set of props that fit it. Since you have clearance with the 15, your Seadrive must have the large diameter gearbox that higher hp engines use allowing for 14-15" dia props.
I will assume that you have the throttle firewalled and only get 4400 rpm. The engine is lugging and you need to change the "gear" in the "transmission" you are using. Since the ratio between the drive shaft and prop shaft are fixed by the engine gearing at 2:1 you are going to have to use your other gear......the prop, or have a look at your procedures.
Reducing the load on the engine goes a LONG way in helping in that situation. This is where proper engine trim comes into play. Proper usage of that function is for best performance of the boat at the desired speed. What works at half throttle may not be what you want at WOT. 20 mph and you are barely on plane (getting the hull on top, not in, the water). If you tucked the trim in tight to get on plane now is the time to push the prop away from the boat to get more of the boat out of the water which will increase rpms and speed. Do you currently use your trim to your advantage, experimenting on what works best under a certain set of conditions...planing out, running at WOT kind of things? If you do and can't get the rpms up any faster than that....and your tach is correct...... you have too much pitch in your prop and have to reduce it.
From what you said you need a significant pitch change if running at WOT and proper trim angle, but I think I'll stop here and let you do your home work and get back on here with answers to my questions and we'll go from there. Were YOU running this boat with this engine before the powerhead change? Were you running this same prop? If so, how were things?
Mark