In this case, you can use Rental Income from the units that you will not be living in and that income can count to help you qualify.FHA rates are going to be lower than conventional for you almost always, but FHA does have a 1.75% funding fee. 

My plan is to set up a syndication fund with Canadian (and U.S) investors to purchase short-term rental properties in the Puerto Vallarta and Rivera Nayarit area (which is booming).

An emergency fund needs to be liquid, and immediately available to you in addition to being low risk and protecting principle. 

The low purchase price, combined with an established market demand, made this an ideal transaction for a fast turnaround and profitable outcome.

LTC is sometimes referred to initial funding.

If you are setting aside funds for capex, taxes, insurance, or other expenses that don't occur monthly, transfer those funds to Savings each month and hold them there until it's time to spend them.

I'm an investor and mortgage broker and have options for loans that go as low as $75,000 and down payments as low as 15%, which makes it easier to stay above $75,000.

Quote from @Fernando Martin-Gullans: Hey y’all, I’m a retail investor with 2 SFH rentals worth a combined ~$650k looking to utilize some of my stored equity to buy more out-of-state properties, but I’m not quite sure how best to proceed given that my interest rates are incredibly low (leaning me away from refinancing) and neither property is owner-occupied (which I believe prevents me from using a HELOC).

There is a lot of public info out there on their funds and how they are (not) performing.  

Hey @Brett RiemensniderThere are a TON of banks/credit unions that will offer as low as Prime on a heloc on your primary residence.