I was in a very similar situation recently, but with Muhammad Ali. His signature has deteriorated very dramatically over time due to his Parkinson's. I had a Sport Magazine signed by Bobby Hull, Koufax, Mantle, Jim Brown, Bill Russell, and Willie Mays. It was missing Ali and Unitas. I went back and forth about getting Ali, because of the signature and the price.
I agree with Mike Navarro that there isn't a personal connection with a mail away item and so I decided to go for it, despite the sig quality. My lovely wife got me the sig as a Christmas gift.
While the sig is small, I am happy with it.
Given the cost is such a big part of your budget, I think Jim Stinson's idea makes a lot of sense.