LLC or S-Corp Blanket Mortgage to circumvent ten property rule

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I currently own 13 single family properties in Columbus Ohio recently appraised at 1.1 million. I have just under 500 K in mortgages. I have exhausted the yellow pages and am searching for this product. Fannie Mae guidelines page 223 say that whatever properties are deeded and mortgaged to an S-Corp are exempt from 10 property limit. However, there are no mentionings of the deed and mortgage in the name of an LLC?
Has anyone done this to circumvent the ten property rule?
I found one lender will do this with over 1 million in mortgages but that's it.
High 600s credit
110K day job
All properties cash flow 400-600 monthly with solid track record.