I am not sure, if I see the issue with publishing the game "prematurely". Is there some exclusivity involved? Your game is "published" on steam since July 22.
Publishing non release game is the usual here. Just publish a wip demo version or early access as steam calles it. Payment is not tied to the status release.
But you do have a point. You should have been warned more explicit, that your game is not "fully" published until manual review.
And, uhm, you actually requested the game to be manually reviewed by making it paid as a previously non payment dev, if I understand the process correctly. If you want to control the actual date the game goes real public, is there not the option to publish it hidden (only reachable via direct link) and change the status later, after review? As I wrote, I see the issue as that you were not aware of the issue while making it paid and not that there are no methods of achieving what you would have wanted to do. But I do not publish, so my knowlege is limited.