The 6 pilots I've known that have flown the Commandant's plane(s) have all been fixed wing - four went their second flying tour and the other two went their third flying tour. It is based on luck, timing and solid performance.
A pilot I knew from my Sacramento was just picked up...dunno if he had it on his dream sheet, but the detailer's called the OPS boss in Sacto, asked for a good pilot who could crush special projects and his name was put out.
I'm sure it's a fun job, and both planes are beautiful, but for me as a second tour pilot and new AC, I felt I should be honing my SAR skills and doing the king's bizness. More power to those that opt to teach at ATC Mobile or Milton, but I wanted to know everything I could about doing SAR, LE, and logistics, and do A LOT of missions on my second tour. Third tour? Yeah, it would be fun (except for flying in trops).