I think you are correct. The rules are determined by the Senate leader and since he has already waived the 60 vote rule (thanks to Harry Reid) he just needs to limit the questions to however many minutes it need be to have the 100 Senators get it done in a week or so. Then call for the vote.
In an earlier post some one said it’s normally about 2 months - so perhaps a vote in later September. McConnell said a vote in the Fall.