There are several avenues to explore. It very well may be true that you will not qualify for a home loan insured, guaranteed, by the government or sold to Fannie Mae or Freddie Mac which limits your ability to get a mortgage. Having less than 10 outstanding loans is another barrier to financing. Selling three of your properties, generating cash and hopefully capital gains, and reducing debt might open up the possibility of a traditional loan.
The problem you face is that the lending market is unusually conservative right now. It is a mechanical rule driven decision process and for most loans lender discretion is not an option. If you do not fit the profile you will not get a loan.
Asset based lending is expensive and unless you have a fabulous deal and plan on using the money short term, under 1 year financially it is probably a mistake.
In all probably there are small commercial banks and credit unions within a 50 mile radius. I am thinking of institutions with an asset values below 250M. My experience is that it is not too hard to reach a senior executive in these smaller banks and discuss short term financing, something like a 3 year 5 year term loan. You will pay an elevated rate above current mortgage rates but not the credit card plus rates of asset lenders. These smaller institutions are looking for and happy to find safe higher than market yields.
I would explore this avenue before looking at other alternatives.
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