You're probably going to have to use a local lender with in-house underwriting. I haven't needed to apply for a HELOC on a rental in a while, but a while back Bank of the West was willing to offer me one.
Another idea is to just move in to your rental, thereby making it your primary residence. HELOCs on your primary residence, as I'm sure you already realize, are much easier to get than HELOCs on rentals. You will probably get better terms too. I don't recall the amount of time a lender might require you to live there before approving you for the HELOC, but that info should be easy to find. After you've lived in your rental for the minimum amount of time, you can use the HELOC to buy the other home you want, rent your rental again, and keep the HELOC. It's a longer process, but it's one way to accomplish what you want.
Thanks,
Robin