What if the Powers that Be behind the new Star Trek Show simply do not tell us which timeline they are using?
Set it a bit in the future, beyond the time of Kirk. It could be set on another ship/space station/Academy wherever. They could still reference Kirk/Picard/Sisko/Janeway because their alt personalities would exist in some form. They could even reference well known missions or events in passing but not mention the outcome so we would not be able to pinpoint in which timeline it occurred. For instance they could mention 'Janeway's trip through the Delta Quadrant' and leave it at that. Any new tech could be explained simply because it is in the future. It could be the future prime or the alt future.
Now it might get a bit iffy concerning things like Vulcan but they could simply...not mention it.
Think they could pull it off? Think of the debates and frustrations. This could keep the fandom busy for years.
I am not advocating FOR This. I'm just thinking of it as one possibility.
Set it a bit in the future, beyond the time of Kirk. It could be set on another ship/space station/Academy wherever. They could still reference Kirk/Picard/Sisko/Janeway because their alt personalities would exist in some form. They could even reference well known missions or events in passing but not mention the outcome so we would not be able to pinpoint in which timeline it occurred. For instance they could mention 'Janeway's trip through the Delta Quadrant' and leave it at that. Any new tech could be explained simply because it is in the future. It could be the future prime or the alt future.
Now it might get a bit iffy concerning things like Vulcan but they could simply...not mention it.
Think they could pull it off? Think of the debates and frustrations. This could keep the fandom busy for years.

I am not advocating FOR This. I'm just thinking of it as one possibility.