As you mentioned, since I foolishly gave QBO a shot, I don't have the Export section showing on my Payroll Settings anymore (screenshot attached) and thus can no longer download these transactions to the updated version of QBDT I just paid $300+ for.

I'd be fascinated to learn how I could even manually export the transactions, since I can't see any way to do that either. 

Failing that, I look forward to a long, long phone call to try and reach your Payroll Care team.