D'oh, didn't really think that one through. I was just going by the usual top stat which is about 36 or so and subtracted for a +6 enhancement item, but forgot that some of those came from inherent wish bonuses, etc. I guess if you start with 18 and add 5 from levels, that takes you to 23. Go human paragon, then Stoneblessed, and that gets you to 27.
5 minutes, 4 rounds from Con. Auto save on Fort for 12 more rounds. That puts us at 6 minutes, 6 rounds. Still not shabby.
edit: with the expert swimmer feat mentioned below, that's... 81 rounds from Con, auto save for 16 more, total 97 rounds. That's 9 minutes and 42 seconds before you start rolling dice.
Then there's that diamond mind manoeuvre that lets you sub a concentration check instead of a fort save. You don't get the secondary benefit of the expert swimmer feat (or do you?). If we can find a way to do it every round, and assuming no twinking of the skill, that's +31 to concentration, or 23 rounds of auto pass against drowning. 104 rounds (10 minutes, 24 seconds), 108 rounds if the feat carries over when using mind over body.