I would check to see whether your current beta test qualifies as a public beta test for Hosted Games’ purposes–typically we see a link on the first post so that players in general can give feedback–that’s what I usually understand as a public beta test.
But I could be wrong–I would check with Choice of Games so that you are definitely conducting the beta that you need to for publication.
This thread is instructive but not wholly the answer: About the Hosted Games Publishing Process