Here in our cold waters many of us don't subscribe to the "cross" of ds/lpi. In a help situation, it prevents you from being able to manage stress on the stage (breathing & inflation) as the second is being used by the other diver...
Whatever you choose, know what you dive....
YMMV
I'm not sure whether you are trying to support or give a contrasting point of view to the previous post(s).
What exactly do you mean by the "cross" of DS/LPI? I run my doubles just as shown in the top picture that
@teknitroxdiver posted. Wing inflator comes across behind my neck, over my left shoulder and down my front. DS inflator comes down behind my left shoulder and around my chest. Is that what you mean by crossing? That the LPI is crossing from right post to left side of body?
Do you recommend having the wing inflator come off the left post and the DS inflator come from the right post?
Your concern is that, in a OOA situation, you would have the wing inflator coming from the same 1st stage as the reg that the "other" diver is breathing from? So, if you add air to your wing at the same time the other diving is inhaling, you could cause the 1st stage to freeze?
The concern I would have is that having the DS inflator come from the right post would mean that it is connected to the same swivel turret as the long hose. I don't see a way to do that where both hoses route well in both the normal positions and in a OOA situation, where the long hose is donated and the turret is swiveled to direct the long hose over your right shoulder, instead of under your right arm.
Also, it seems like, generally, if you get into a "situation", first, you would presumably be neutral or very close to it at the time. So, you probably wouldn't need to be adding air to your wing. So, the concern of adding air while the other diver is inhaling seems pretty low risk. Also, if you're really worried about that, you could just add a little air to your drysuit, instead. I mean, in that scenario, you shouldn't be needing to add much air to either, right?
I know I don't have the same kind of cold water experience that you do, so I'm really not trying to argue with you. Just thinking out loud, so to speak, as I try to understand all the subtleties of what you're talking about.