I even went pawing through the '08 Handbook to see if maybe there was some mention or clarification on this, but couldn't find anything.
I'm a little surprised that there is no mention of this particular situation, which I would imagine an EC doing Resi service work must come across at least occasionally in the field.
If it were just a short NM cable run in an open basement, I guess replacement of the cable wouldn’t be that big of a deal, but if it were a second floor area or something similar, then we're talking major work.
I suppose if you snip off the grounding conductor, frown then technically it is not "present in the outlet or junction box" as stated in 250.140 Exception, so you could keep the three-wire receptacle configuration using the grounded conductor to ground the dryer frame.

Apparently, it seems that it comes down to a judgment call as to which method is considered safer and more compliant, since for the last ten years or so, the NEC has been steering us away from using the grounded conductor for this purpose.