Possible Way Around the Regeneration Limit

As many of you are aware, it was stated in the classic series that Time Lords can only regenerate twelve times. After that, they're as mortal as anyone else. Given the recent reveal that Matt Smith's Doctor has regenerated eleven times, and not ten as previously thought, then it seems the upcoming regeneration this Christmas will the be last.

If Moffat wants to continue the show after Peter Capaldi, then he's going to have to find a way to eliminate the twelve regeneration limit. People have proposed that when River brought the Doctor back to life in Let's Kill Hitler, she gave him her remaining ten regenerations. Moffat could do that, but it would be more of a stop-gap measure that would simply punt the issue thirty or forty years down the road. What would be better is if he could find a way of using the Doctor's statement in Death of the Doctor that he can regenerate 507 times.

We already know from A Good Man Goes to War that Time Lords evolved their capability due to exposure to radiation from the Untempered Schism over billions of years. What I propose is that they gained their regenerations slowly, one at a time, over billions of years as they were exposed to more and more radiation. By the eve of the Time War, they had evolved twelve regenerations. During the war, they realized twelve wasn't enough, so they exposed themselves to more radiation and sped up the process. By the end of the war, the Time Lords (or at least the Doctor) had upped the limit to 507.

Given the tenure of the typical Doctor (three to four years), this would punt the issue well over a thousand years down the road. By the time of the 36th century, either the human race will be extinct, fiction will be a lost art/illegal, the show will have been cancelled anyway, or the writers will have had 1,500 years to think of a permanent solution. Either that, or everybody will have forgotten that the Doctor was only supposed to have a finite number of regenerations in the first place.