Routes out of New Orleans at the choke points:
To the northeast:
I-10 - 2 lanes eastbound
US 90 - 1 lane east
US 11 - 1 lane east
To the north:
Causeway - 2 lanes northbound
To the northwest:
I-10/55 - 3 lanes northwest to the split, then 2 lanes each (I-55 to Jackson, MS and I-10 to Baton Rouge), plus 1 lane north on old US 51 parallel to I-55 after the split.
US-61 (Airline Hwy) - 2 lanes northwest
River Rd/Spillway Rd - 1 lane northwest (a local road running through the river communities and across the wide spillway on the east bank of the Miss. River)
On the west bank of the Miss. River:
LA 18 - 1 lane to the northwest
LA 3127 - 2 lanes northwest
US 90 - 2 lanes west to Lafayette and I-49/I-10, but also drains Houma, Morgan City, and New Iberia
While some of those will flood earlier, others can have their inbound lanes converted to outbound, nearly doubling capacity, plus some have wide shoulders(until breakdowns start to block them.) IIRC, freeway capacity per lane is usually between 1500-2500 cars per hour, depending on speed. At 10 mph a lane should still move 1800+ per hour.
It's been a while since I lived there, but what are the chances of them turning all the I-10 lanes westbound out of town all the way to Houston? It doesn't sound like it will happen today, but maybe tomorrow? The outer bands should start hitting by then, and maybe it will sink in.
Of course, it may hit Mobile too, and I'd look like an idiot, but better safe than sorry.