We are scrambling to get more vacant apartments for all the applicants.  

But after one month, only received one unqualified application.

But I showed him my first property, the numbers, my Cozy account, how I was screening tenants, my leases and applications, bank accounts (showing I was running it separately of my personal finances), and some bigger pockets calculator results.

Im assuming you will not have a Property Manager make sure you have your systems set in place beforehand (concerning how to handle maintenance request, rent, applications  etc) and that you understand your State Tenant & Eviction Laws..

Before submitting my application, I would like to know whether it is at all possible to use an FHA and get around the required residency?

Application fees (over $100) or any form of commitment fee are very suspect on smaller deals meaning under $1million.

A HUD housing voucher should be viewed as income that would count towards your “standard income qualification” for potential tenant applicants.

Load properties, market them, screen some fake applications, move the person in, accept rent, edit the ledger, enter/track maintenance, how does it handle tenant communication, run all the reports to see if they provide the information you want in a professional manner, etc.You'll narrow it down to a clear winner, then jump all in and use it.

That means the owner with more expensive properties will have fewer well qualified applicants. 

You just create a form with the relevant information like date, address, applicants, amount etc.YOU OR YOUR COMPANY accepts "HOLD DEPOSIT" monies from Applicant(s) as a non refundable intent to rent fee for the property listed above and funds will be deposited into a deposit account serviced by an agent for Owner.