@Christina P. Okay, no worries most lenders would allow a transfer of stocks/mutual funds into a checking account to cover closing costs. Guidelines vary from lender-to-lender.
HELOC's work great if you need to borrower money for a short-period of time (due to the higher, variable rates). Also, If you intend on paying off the HELOC within a few years, it might make sense to go that route.
However, based on your scenario, it seems like you would probably hold onto the loan for longer than a few years. Furthermore, you wouldn't be spending portions of the balance periodically (and only paying interest on the money used). On the contrary, you'd be using most (if not all) of it at one time to cover the closing costs of the new purchase.
Rates are still low, but they're on the rise. I'm curious what rate you would qualify for on your primary home and what the actual payment difference is per month. What state do you live in?