Work with a professional 3rd party PM who already manages dozens or hundreds of S8 units and is on a 1st name basis with the local case works/housing authority folks.

If this Lease is not accepted by Landlord or Landlord's authorized agent within five (5) days, the Initial Deposit shall be refunded."

I noticed that for last quarter of 2023 I didn't receive rent from the housing authority.

You might want to check with them and see if there is that much demand.That is definitely a niche product and you are a saint if you want to take on 200 Section 8 tenants and housing authorities. 

I've spoken with the local housing authority, but I am noticing some inconsistencies between guidelines and what the people at the authority told me.

Housing authorities are non profits and I know some are bigger than others.  

However, specific regulations may apply, and it's advisable to consult with a legal expert or housing authority to ensure compliance and handle the situation appropriately.

Since the scammers are overseas, authorities can't do much about it after the fact unfortunately. 

If so, how do you secure the authorization on their card past 30 days?

You may easily look up the person on the NMLS site with their licensing number and find out if they are authorized to conduct business.