My third book is due out soon and I'm discovering a curious problem between the ebook and the print book. Since I'm guessing there are at least a couple of people around here who self-publish

I thought I'd ask.
I hire an artist to do the cover. They do some work, I approve it. Yay, cover!
Now, for the ebook, we're ready to go. The book is done, so just click Publish.
The paperback version, though, needs work. Because the artist cannot produce the paperback cover until they know the page count. And I can't tell them that until after the final proofreading run, which means not until after the book is Really and Truly Done. IOW, mere hours before I can click Publish on the ebook. But the artist, bless 'em, evidently does not sit about awaiting word from Yours Truly; they have other clients.
So it's a week, maybe two or three, before I can produce the paperback. Then I must order an Author Copy so I can do what they used to call proofing the galleys--verify that the physical artifact is what I was expecting. A delay of more weeks, even assuming the Author Copy is perfect.
That makes it a month or thereabouts between the ebook and the paperback. That seems crucial to me. Those first days are my few days of sunlight in the Amazon Ocean before I sink again into the briny deep, and there are still plenty of people who like to buy physical books. They notice me, they think hmmm interesting, only to discover there's no paperback available. Wait, don't go! Aaaaaaah! Lost forever.
OK, maybe a tad dramatic (Tad Dramatic would make a great character name), but I wonder am I worrying over something real? Have others run into this? Any strategies or solutions?