This page has good PageRank, so I thought I’d add my experience:
I had the same problem on a different jam. Game was published, page public, but not pickable. I recreated it with a new project without filling in all the fields and was able to choose that one.
I think it didn’t show up in gamejam picker because I’d initially set Public with “Don’t show in search”. I didn’t do that on the second and it worked.
(Also, my second project had the same name as the first. When I added it, both were submitted to the gamejam.)