Hi,
I don't wanna put you off, I like the ideas, and I did'nt know that about sea turtles, but I think it's a dead-end.
I don't think that information about aborving O2 through the trachea will help anyway, since if it's O2 in air, it's intouch with your lung tissue anyway, so you will abosrve it eventually (it's in the same air-space). And I would never wanna have water in my trachea, that's how drowning starts!
About the stomach: it has thick walls and mucos (I think) that are supposed to withstand acidity of PH 1 or so, and produce acid themselves, so I doubt if any gas transfer is possible there. and even if a minute amount of O2 could've been absorved to those near cells, it would'nt have left to the blood and transfered to where you really might need it.
Absorving O2 from water through nose tissue, if possible, will probably require to circulate it otherwise the amount is so minute that it doesn't worth bothering. Think of how small surface area the nose has with the water compared to your lungs, and that it has considerably much less blood flowing through it, and that water don't have as much O2 as we air-breathers are used for...
I think it's a dead-end no matter what.
But if it can be done, I think that breathing in and out small amounts of water to your nose for circulation (and thuss small amounts of air to your lungs) might signal the body that you've started breathing again and will raise the pulse and make you lose more O2 than you gain, same that happens when you 'pump' your mask during the dive (not during the ascent). Might make you feel a short term relief though. If you could circulate water in your nose by expending/contracting your mouth space.... I still doubt it much, but who knows?
Yet I think I'll stick with improving using the more conventional methods for now...
Regarding 'anus breathing', there's a limit to what one might sacrifice for a few more seconds underwater, but you are welcome to experiment.