There are few options Jarid,
Can you get a co signer? (family member)
Partner with someone
Join a syndication or partnership on a deal as passive investor.
Start smaller, buy one for cash using the HELOC and do the BRRRR strategy.
Pull your money out by 6 month and repeat the process.
@Jarid Reeves , If your serious then get out of the business of renting from yourself. Sell the house your in (if you've been in it for 2 out of the last 5 years then all the gain is tax free), rent a modest home banking 2 years rental. then go find an owner carry situation with that large down payment and let rentors start paying you.
Personally love having my home free and clear. However, I probably am in a different stage of life that you are. If you are hell-bent on pulling money out, @Hadar Orkibi has a good point on the heloc or refi that you can sign for YOURSELF.
And I'd target deals that the seller will finance, OR, get private money (not hard-money) and give them say, 6--8% interest only for x (maybe 5) years. Work on getting your credit and income up, then you can refi out of the private. Rinse and repeat.
if you buy right you should be able to BRRRR the property. this way you use the money of the HELOC but after the refi you pay it back to yourself. pay the debt down again.
you need to be firm on not to use the HELOC on liabilities, Holidays and cars etc.
Private money would be good option, but its relationship based transaction so dont count on it. Seller financing or BRRRR with HELOC will be easier.
Sell your home to access the equity if you can not refinance or get a HELOC to pull the equity. Renting is far less expensive than home ownership. Your equity is dying a slow death sitting in real estate.