A great REALTOR will help you gather rental history and the cost to own and show you good sites for pulling rental projections, but you will need to do your own calculations.Everyone's mileage varies.

Verifying last 2 years of rental history very important!

If they don't have prior landlord references, that's a valid excuse for not moving forward with their applications - you simply want more rental history.

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

I'm just buying my time and making some connections while I build my credit history again - worst part about moving country haha!

You could likely get into a rental with a DSCR loan at 20% down, which would be similar or less in terms of DP on an owner occupied loan via conventional financing in eastern MA. 

We are only allowed to screen non-tenant applicants for criminal and rental history, nothing financially related. 

It depends on how the transaction is structured, and the history of the title and timing. 

At every point in history of the 15+ years of the site I've noticed the old timers complaining that the site is the worst it's ever been. 

This could help secure a higher LTV while you build STR rental history.