Re: alpha one vibration on turns
Alignment is CRITICAL! Don't bother replacing or servicing the drive until you make sure the engine is aligned properly or you'll be right back where you started.
If the noise and vibration you're getting isn't happening all the time and only happening in the turns, check the coupling between the engine and the driveshaft. They do wear out and will cause noise and vibration in the turn when the driveshaft gets side loaded. When was the last time it was greased?
I wouldn't consider the amount of play in the prop shaft to be cause for rejection unit you measure it. Side to side play on the prop shaft is allowed to be max of 0.003" and runout of >0.007" indicates a bent shaft. End play isn't really discussed in the manual and I'm pretty sure what you're seeing is normal. Mine does the same thing... I'm sure one of the more knowledgable guys here will chime in if I'm gooned up on that.
Rebuilding the lower unit is possible, requires a few, fairly spendy, special tools and some know-how. Measuring the backlash and setting the pre-load is tricky business.
A replacement lower unit might be the way to go if you're not up to the challenge. Assuming this drive is an Aplha-I, SEI
http://www.sterndrive.cc/index.htm has them for fairly reasonable ($800) and they seem to get good reports.
Also, you'll need to figure out the source of water intrusion... do a pressure test.