Maybe PA/the county you are in are faster, but 4 to 8 weeks is usually what I have seen.

Recently we've;1) Introduced them to property management software for their self-managed properties allowing them to collect payments faster, screen tenants efficiently and track expenses more accurately.2) Begun screening for new property management of the 5-unit property.3) Started gathering documents for potential lenders. 

Any recommendations on getting a HELOC on my residential home to pay off the debt faster and use the equity to purchase my first multifamily investment?

Would have "flipped" this one faster if we weren't working 2 full-time jobs, raising 2 boys and pregnant with another one.

I'd rather move to bigger, faster-growing cities like San Antonio (has my heart, only 2 hrs away). 

This will be faster than a 30-yr, with lower up-front costs, which I think will more than offset the slightly higher interest rate.

Getting skin in the game will help you learn a lot faster and with real experience, which is always better than imaginary scenarios.You can do it!

Now I'm looking for my second property, but it doesn't seem like anything would even break even since property values have risen much faster than rents.

I also think it would happen much faster than 16 years, mostly because your average of $20k is low, maybe at first, but once you start taking down bigger deals, profit will go up (assuming you don't have a huge uh-oh).

Perhaps consider staying longer, paying down your mortgage faster, refinancing, so that when you move out in a few years, the mortgage payment is lower and cash flows better.