Using foreign income to qualify

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I have what is essentially investment income from non-U.S. assets (not a brokerage account) that I was hoping to use to qualify for a new mortgage. I literally receive a foreign check in the mail every month, which I deposit into my personal bank account at the current exchange rate. I pay foreign taxes on it, have check stubs going back several years, and get an annual foreign tax form every year, similar to a 1099. The trick is, you don't see the income on my US tax return, due to a weird complicated bit of a US tax treaty that treats this particular income a certain way.

I've read through the income criteria for both FHA and conventional loans in the HUD and Fannie Mae handbooks. Both of them address the situation of how to qualify investment income, as well as foreign earned income. Problem is, this doesn't fit either of those exactly. It's foreign, but it's investment, not earned income.

The current lender I'm talking to has said they can't use it "because it's foreign". I pressed the issue, and they couldn't give me a good explanation of SPECIFICALLY why they couldn't use it, other than "it's foreign".

I've talked to two other brokers, one of whom didn't think it would be a problem, and one who wasn't sure and said he could submit it to the underwriter for a pre-approval to find out. I'm just afraid that I'll end up going with one of these guys, letting them pull my credit, and then find out that they won't accept it after all.

The HUD handbook for FHA mortgages says that investment income can be verified from tax returns or account statements, and it doesn't specify U.S. or foreign.The Fannie Mae guidelines say something that's essentially the same.  I would argue that means it should be used, since I can show monthly documentation, foreign tax forms, etc.

Anyone have any insight on this, one way or the other?