Well it's been 7 years since anybody posted on this thread and I still thank all of you who did because I have just run across the same problem on a TomCat we just bought. One of the reasons I chose a CDory was the existence of this community. It really helps in situations like this. I have 2 of these 150's so double the risk for me.
Sandy, if it makes you feel any better, I did spend the money on an motor survey from Master Marine in Mount Vernon, Wa. and they did not catch it. I took it on a sea trial and also missed it myself.
I never owned an outboard motor before so I did not really know I what I was listening to, but right after I bought it I noticed a whine on one motor that I did not have on the other. I was hoping it was just a belt but some research indicated it could be something worse so I took it in to somebody who knew what they were doing. He concluded this was the problem and showed me about 1/8" vertical play, so not as bad as yours. The only symptom I have so far is that whine. I am hoping I caught it soon enough for the easier fix mentioned above.
My plan is to see if I can get it fixed without replacing the whole motor and then call Honda, as some have suggested above, and see if they can help me out. All great ideas. These motors are at about 1000 hours.
Bob Switek