avrdude: stk500_getsync(): not in sync: resp=0x30

There seems to be so many 1000s of people having the same problem

It's not "the same problem." It's a generic error message that gets reported for LOTS OF DIFFERENT PROBLEMS.

I'm pretty sure that the R3 boards have the same bootloader and speeds as the previous Unos.

To the person with the Zumo shield - does it start working if you disconnect the shield?

As the nominal "owner" of Optiboot, I'd be willing to expend some effort to debug some of these mysterious failures (especially the ones that went intermittent to solid broken), but doing so over the net seems hopeless. I'd need to have your physical board in my possession, and since I'm not a "vendor" I can't offer a replacement board or anything while I work on it. I'd be willing to mail it back if I get it working, though.
So if you're willing to mail me your "dead" arduino for debugging, or if you're local to the SF Bay Area and have one of these consistently failing boards, PM me for contact info...