Hey Corey,
I guess it all depends on your longer term goals. I wonder if you could qualify to get a home equity line even if you didn't pay down your loan with your own cash? That would be the best of both worlds, since you may have twice as much capital to use to invest in other real estate.
If you were to use your cash directly for the new investment, you wouldn't have to rely on a lender at all. Plus, if you pay down $30,000 you may only qualify for a $30,000 or even less depending on your equity position.
I'd suggest approaching a lender to see if you can get a HELOC now. Some lenders will give you up to 90% combined loan to value. Meaning if your property is worth $100,000 and you currently owe $60,000, they may be willing to give you a $30,000 credit line for a total loan to value of 90% between both of your mortgages.
It's always better to have the money available before you find the right property. We've used HELOCS and cash out refinances to fund the purchase of new deals. It's a great way to leverage your assets. For alternative ideas to get cash, you could borrow against your retirement or take out a cash out car loan, if you have equity in a vehicle.
I hope this helps! Let me know if you have any more questions. : )
Ashley