I have LOCs on several of my properties but I had paid cash for them and had no other financing. I forget what LTV they are but if you already have loans on the properties, I doubt anybody will do a greater than 75% LTV LOC. If you have had good appreciation since you bought, maybe. But there are going to be flat fees that will make a small amount even more expensive.
What about saving up the monthly cash flow instead of investing it at Vanguard? Yea, I've been in cash a lot through the stock market run up but those are funds looking for a home in real estate instead of being able to be invested elsewhere.