I reckon Craig Caldwell's 1 year and 1 week is the next best effort. This is described in his book Climb Every Mountain, where he tackled all the Munros and Corbetts in '85/'86.

There was some talk of an 85-day round existing, but this doesn't seem to be documented anywhere so Caldwell's round seems to have been the fastest known to date. It would be good to get input from forumites to correct or confirm this.

The fact that there have been so few attempts to date might indicate the level of difficulty involved! (Contrast with the number of known fast Munro rounds.)