For a vintage HOFer, getting a GU shirt for $1,000 isn't likely, but I have recently found 2 HOF flannels for $2500.
The first is Gaylord Perry, although it has a team number change. It's in otherwise good shape:
https://www.ebay.com/itm/144531223602
And I picked up a 1971 Jim Kaat home flannel last July in a Hunt auction for about the same. Of course, nobody was certain Kaat would make the HOF at that time.
In short, if you increase your budget a bit, and especially if you're willing to delve into the more modern knits, I'll bet you can score a HOF jersey that could really be a collection centerpiece item.