Based on that, I can see that demand is high and I probably have potential to increase the rent.Best of luck!

That brings their total return up to $64,400/yr or a return of 47.7% per year (I know, I know, I didn't factor in the increasing cashflow - I did that to be conservative). 

This doesn't mean you shouldn't offer but have reasonable expectations on chance of acceptance, my gut puts your odds of getting the property at 10-15% Can I increase my chances if I write a letter to the bank?

Nicholas,call a loan officer and give them your numbers, they will be able to tell you how high your second VA loan can be, if you need more then that, you can also do a downpayment and increase your loan amount.

This creates two challenges for me:1) I'd like to do moderate to significant renovations on the units, and my business partner plans on owner-occupying one of the units, so we would need to permanently vacate one or, depending on the property, even all of the units. 2) In order to make the numbers work I'd need to dramatically increase rents (by several hundred dollars/month) to bring them up to market levels. 

A big advantage of real estate is your risk drops quickly as your knowledge increases. 

If you make renovations and/or additions to the property which will increase the value of the property, it is possible to refinance and pull equity out. 

I would be more likely though to find a way to market the apartments to law enforcement to increase the probability of a law enforcement officer moving in.

Does any one have experience purchasing a VA loan backed property utilizing an ARM and then refi'ing into the IRRRYL before the rate increases? 

Howdy @Ryan ClevengerBesides living in it for one year you will have to figure out how to increase the equity in the property.