Does Chronobooks allow you to pick and choose what you want to copy to a new company file from a backup?

Afaik, there is no such feature yet. You have to full restore it prior to copy the selected data to other account.

https://www.chronobooks.com#_r_chrono

Thank you for posting in the Community, @DSinghSolar.

I'd suggest contacting Chronobooks since this is a third-party app from QuickBooks Online. To check if this feature available.

Please check out this link below about ChronoBooks app. 

•  Do More with Apps: ChronoBooks  

Please let me know if you have other questions about ChronoBooks. I'm just a post away. Happy Holiday!