Re Post production periods
I don't know a whole lot about them as they tend to be behind closed doors, but looking at his discography details, most albums he has worked on were mixed at different studios than they were recorded at, by his in-house engineers (Todd Monfalcone and Kennie Takahashi) or with them in conjunction with the band's chosen engineer, e.g. Tchad Blake on the Black Keys' most recent record.
An article about El Camino (the most recent Black Keys' record) and anecdotes from people involved said that DM reviews and approves the mixes as they're being developed. But he doesn't have to be in the room for that, necessarily, living as we do in technologically advanced times.
As for the period of post-prod, it's a little hard to say because his projects tend to overlap, and a record might be 'in the can' and waiting to be released when the marketing powers that be feel it's optimal.
But, for example, principal recording for El Camino wrapped up around the beginning of June 2011, was reported to be 'done' that summer, and released in early December.
The Broken Bells record was done recording sometime in the Autumn of 2009, mixes were finalized later that winter (we know they weren't final in January because an unfinished copy of the record leaked then) and it was released in March 2010.
Though both of those records were on major labels (Warner and Columbia respectively), the machinery behind them would be dwarfed by the U2 juggernaut, I'm sure.