We were in New Orleans for New Year's - I reread your post just before posting, so I see you're probably familiar with lots of this, but here are some low carb possibilities from our trip:

Acme oyster house – raw oysters w/squeeze of lemon (approx. .5 carbs per oyster)

shrimp remoulade (remoulade is a spicy mustard sauce, but in most incarnations it's really not high carb - just don't smother the shrimp) - in lots of places

any seafood dishes that aren’t breaded or with pasta - lots of good choices

Brunch at Brennan's would be a wonderful splurge that could easily be done low carb, so long as you don't mind skipping the bananas Foster.

Lots of walking, even a walking tour of some of the cemeteries or of the French Quarter or Uptown, should help. I found it difficult to keep up my water intake while I was there, and I put on a few pounds of bloat, but it came off quickly when we got back.

Can't help you with Bourbon Street - we avoided it like the plague!