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I'm not hugely knowledgeable on GMB, but no I don't think that GMB checks an associated / verified website, and then uses data from within it to sort its own internal GMB listings. I could be wrong, so I'd wait to hear from a couple of others. As far as I know though, GMB rankings are affected by GMB data and wider-web rankings (on Google's main search engine) are affected by a rich mix of data, including open-web data. But GMB rankings, are not (I don't think) affected by open-web data

Honestly, if the client is already on you about not losing SERPS, I'd just leave the structure as it is. Preserve it and move it over to the new site. It's not as clean as you would like it, but it does contain the blog title in it and that should contain relevant keywords/subject matter. Can you expand on the 404 issue with Hubspot scheduling? Have you talked to them about this issue? They're pretty adaptive and I'm surprise their scheduling structure would produce 404's ahead of the post being published. I hope that helps!