Well, at least the problem with the 5d III can be corrected over time, and at around $2900 new this issue may already have been fixed. Fixing an underspec'd 6D on the other hand ... not so easy.
But it is - sell the 6d for €1200. The 6d as well as the 5d3 have weaknesses, obviously the 6d more than the 5d3, and "underspeced" for the 6d is only related to the competition (d600) and the current price. Just like the 5d3 is also just another camera and there are better current models (1dx) and there will be newer replacements to come, maybe sooner than later.