I was probably a family member, who doesn't need a good credit score.

that we’ve learned in our 24 years, managing almost 700 doors across the Metro Detroit area, including almost 100 S8 leases:Class A Properties:Cashflow vs Appreciation: Typically, 3-5 years for positive cashflow, but you get highest relative rent & value appreciation.Vacancy Est: Historically 10%, 5% the more recent norm.Tenant Pool: Majority will have FICO scores of 680+ (roughly 5% probability of default), zero evictions in last 7 years.Class B Properties:Cashflow vs Appreciation: Typically, decent amount of relative rent & value appreciation.Vacancy Est: Historically 10%, 5% should be applied only if proper research done to support.Tenant Pool: Majority will have FICO scores of 620-680 (around 10% probability of default), some blemishes, but should have no evictions in last 5 yearsClass C Properties:Cashflow vs Appreciation: Typically, high cashflow and at the lower end of relative rent & value appreciation.

Or how to put the unpaid rent on their credit score

Depending on your credit score in the US and credit trade line history, you could put as low as 25% down.

You can do a duplex though, which might not be a bad idea.With your credit score, conventional might be a good choice, you only need 5% down for 2-4 units if you live in one. 

Is there a benefit to foreign national loans for a US citizen with a US credit score (the 791 I mentioned in the original post is my American score)?

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Also credit score 680 with no missed payments over the last 2 years and also check their criminal report just to make sure you know who these tenants are, as the eviction process in New York city is very long and expensive. 

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Taking on issues the seller is not willing or able to cope with can score you a better deal.