Hey Rob,
This is a good question, and I suppose my short answer would be no $2,618 is not a reasonable amount to expect from HANO.
There are a couple of factors to take into account when looking at the amounts HANO is willing to pay, and I provided a few items below.
Correct Voucher
If you are wanting to rent out a 4 bedroom home, you are going to want to make sure that the potential tenant has the appropriate voucher. It is often difficult to find tenants that specifically have a 4 bedroom voucher, in some cases you will have interested tenants that only have a 3 bedroom or 2 bedroom voucher. These circumstances would obviously reduce your potential rents.
Must Qualify as a Bedroom
To qualify as a bedroom for HANO's purposes you must have a closet in the room. Often times in New Orleans I have found not all rooms have closets.
Zip Code Consideration
Looking at Zip Code 70112, you can see that it includes areas that span from the Quarter to the Treme area. The price HANO is providing is quite high if your property is anywhere outside the Quarter, however, it might be more reasonable if you are talking about a property within the Quarter.
HANO Guidelines
I've provided the link below, but here is the important part: "To calculate the approved rent, HANO compares the owner-requested amount to the rents for private units with similar features, amenities, and location." They also mention the Maximum Initial Rent Burden: "The approved gross rent (owner requested rent and the HANO allowance for tenant paid utilities) cannot result in the tenant having to pay more than 40% of their adjusted monthly income toward rent."
http://hano.org/Landlords/Payment
Maximum Initial Rent Burden
I haven't looked at this in depth before, but this qualification seems to make those prices an impossibility. At $2,600 a month rent the tenant is paying $31,200 annually, and to qualify to pay this amount it has to be equal to 40% or less of their income. Meaning, the tenant would have to make at least $78,000 a year. (31,200/.40) = $78,000
This would disqualify them for assistance most likely if they were making that kind of annual income, and assuming I am not missing anything else.
My HANO experience has been poor. I've had good and bad tenants, mostly the latter, but the vetting of potential tenants can help a lot. The initial process to have a lease signed is more cumbersome with HANO than if you were to sign a lease with a non-HANO tenant. Overall, it is HANO's job to protect the tenant and their priority is the tenant, and it was this realization that led me to my current poor opinion of the organization.
My personal estimate of rent varies by condition of the property, location (down to the cross streets), and current market prices. I'd look at Craigslist to do some price comparisons of the area considering potential affects of the market from COVID-19. Rough estimate of monthly rent to expect (1400-2200).