Chaining HELOCs to delay conventional mortgage limit caps?

[Michael B.]

I currently own ten rentals of which nine have conventional mortgages.  I know I can get a 10th mortgage before I can no longer get a conventional mortgage.  I realize that at that point most people go with a portfolio lender, but I was wondering if I could shuffle stuff around to open myself up for more conventional loans.

I've read a few posts about it being hard to find HELOCs for investment properties, especially when over four mortgages, but let's assume I can find a lender to loan at 75% LTV. Could I get a HELOC for the sold off house at 75% to pay off mortgage #1, then the other 25% for a down payment on new mortgage #10? Then do this again for #2, #3, etc.? I realize that once I get to the newly purchased houses I likely wouldn't have enough equity to continue, but at least for the ones I've owned for years I could likely buy myself some additional time until

Basically I'm trying to convert conventional mortgages over to HELOCs.  Would that then allow me to get ten more conventional loans?  Am I missing anything, aside from the challenge of finding a lender?