Wow, lots going on here. I think I skipped over this thread initially because I assumed it was a kettle souring question
Collaboration sounds cool, and good on the brewery for being open to this. I'm a little surprised that they seem to be ceding so much control over the batch. I hope they have good sanitation in place, etc.
One thing that I'd be concerned about is consistency from batch to batch, if the brewery decides to continue with this after the first batch. If this is just a one-off special brew, not as critical. (Kettle souring would be more repeatable though...)
For you personally and in case the brewery wants to keep this mixed culture going after the first batch, there's a great AMA thread with Jester King head brewer Garrett Crowell where he discusses how they store and handle their house culture (which was started from a mix of commercial pitches, wild-caught yeast, and bottle dregs). See the last post on this page, among others in the thread:
Garrett Crowell AMA
Is the recipe basically a pils/wheat combo? If you're concerned about the beer being too thin/overly dry, I would recommend mashing high (156-158 even). The higher you mash though, the longer it might take to reach FG. Does the brewery have a turnaround time in mind? Or are they open to waiting it out?
Not sure about the nitro idea, but maybe they can try it out with a single 5 gal keg to see if it works.
What kind of barrel is it? And if they already have the barrel, what are they doing with it until it's filled? Unless it's a wine barrel, I'd be wary of using a freshly dumped spirit barrel for a sour (esp a lighter sour).
Sorry for the long response