I also have the same exact issue with the "Project" data from paychecks not showing up in the Project.  The timecard shows up there though.  Was is beyond frustrating is I have been on multiple calls with Quickbooks and they never mentioned this was a known issue.

So many wasted hours on this issue.  I will have my case updated with this information as I am not the only company having this issue.  I am a ProAdvisor and only one of my clients is affected.  They are on QBO Advanced and Payroll Premium. 

I have also tried to restore to backup 28 times!   That feature doesn't work either.