Say I'm able to complete the refinance, I would then like to immediately apply for a pre-approval with the intention of buying another property as an owner occupant via FHA financing as my family size will be increasing in 6 weeks and I will need more square footage in my living space.Is this something I could do? 

This book truly changed my life, so much so that I bought a copy just to give to my brother in the hopes that he at age 27 could take advantage of what I'd already passed at age 31 (he's single and doesn't own a house yet, whereas I'm married and have a home).I have to admit, when I started listening to and reading Bigger Pockets I was thinking all about increasing earnings and didn't understand why I would "rob" myself in the mean time and be "needlessly frugal."

For example, if we got a $100/mo raise (after tax), we might increase our monthly expenses by $50.   

Over time as my cash flow and income increase it’ll become easier and within 5 years of starting I should be buying 5-6 properties per year.

Especially with only 15% down.I've been seeing 10 year interest rates creeping higher and higher above 5% over the last few weeks.   10-year Treasury is at 2.77% today, so even 5.10% is only ~230bps.   30 year amort is also becoming increasingly scarce on smaller deals.  

Perhaps fix up a couple units, increase rents, live there for 1 year, then move on to the next multi family.

In a rising market, I personally wouldn't want a 3-year lease - unless it allows for incremental increases in rents during the lease term.

NPV gives you a dollar figure that represents the increase  (or decrease ) in cashflow for the term of the investment. 

@Tamara Smith Short term rentals can be a great way to increase your cash flow, but be careful about the specific locations you choose as the laws for each municipality are different.

Those where the rent has increased but the value has not, hold.