Thanks for the tips on how to reach a human - that's so valuable in seeking support!

Here's an update: the screen going blank upon logging in to QBO using IE 11 is a "known issue" at Intuit.

Regrettably, several weeks later, it is still unresolved.  Without this capability, QBO can no longer be exported to QBDT.  When or whether, if ever, Intiuit will fix this issue, is unknown.

I took the case all the way through to Data Services, who are next in line behind the engineers, in understanding how everything works, and they said they would add my name to the ongoing "investigation," to be notified when thee issue is fixed.  I'm not holding my breath.