@Alan Brown I buy dozens of houses every year and I don't use a dime of equity in any of my existing portfolio.
There was a time when I was struggling with mounting debt and little deal flow. I had done exactly what the OP had done; taken multiple HELOCs on my rentals to buy more rentals. I called another mentor and told him my challenge and how I thought I might fix it - borrowing more money. He said to me; Aaron, never borrow your way out of a problem. Think your way out of it. So that is what I did.
My portfolio could take a 50% loss in value and I'd still be fine all because I don't use my existing properties as ATMs to buy more properties. This also keeps me from doing marginal / bad deals since I have to work out solutions to acquire new houses using new money, notes or terms.
I know lots of investors who have much higher net worths than mine and many more properties, but what they also have are millions and millions of short term balloon notes securing all those houses. If the market stays strong, they'll look like geniuses, but if it flattens or slows down, they may be helping me pick out a toilet next time I go to Home Depot.