We've been able to fund foreign nationals with absolutely no U.S. credit. 

National banks, credit unions, mortgage lenders and the like.

There are investment property DSCR mortgages for foreign nationals.

Assuming you're looking for a fixed rate permanent loan on a stabilized property, I recommend regional & national banks.

When not 'full income' verification, which can even allow for high 55%+ DTI there are alternative income verification guidelines like bank statement, P&L, DSCR, Foreign National, Asset depletion, bridge and portfolio programs that allow expanded ways for borrowers to qualify. 

For me personally I like mid-sized/regional bank as you are not just a number like with a national bank, but they still have some of the bells and whistles like good online tools that small banks lack.

Columbus is also home of The Ohio State University, one of the largest universities in the nation, which currently building a $1.79 billion inpatient hospital expansion.

and have been having difficulties passing the national portion does anyone know if the national portion ask some questions that are state specific?

I myself chose the suburbs of Youngstown Ohio to get started in, statistically one of the least desirable metros in the nation.

Also i would highly suggest you don't only shop the small banks shop the national ones as well.