Based on my recent experience in NOLA, they could advertise $3,200 per day and it wouldn’t have mattered. Can’t rent what you don’t have. I’ve completely recalibrated travel protocol in the last 9M or so.
Try the public bus. It's probably quite cheap and goes via SkyHarbor Airport. I do the bus thing a lot in cities I visit. It's mostly normal people and safe. (I like to save $, I was on the TCU Ed Investment Fund back in the day, and the less I spend, the more "mad money" I have to invest. Frugality rules in my book!)