Are you wanting to deposit first or request first? Most people request first that way you only give up your points if and when they find what you want. The main reasons to deposit first are if you have points you would lose and don't want to (or can't) rent them out. The other reason to deposit first is if you're looking to use an off season HH deposit and want to guarantee the lower points total.
Excluding Mardi Gras, NO is still a hard exchange but doable if requested at least a year or more in advance. I'd look for an owner there and try for an exchange. Maybe giving up less than a week or a smaller unit. To do this, you might go to TUG and look at the direct exchange info, only $15 for year one.