This allowed me to get a construction loan to repair the other buildings and repay my investment into the property.

I'm using my VA loan so I don't have to put any money down & can keep money in my account to fund rehab deals. 

Focus on the big-ticket items and estimate costs.Financing: Whether it's private money, hard money loans, or a traditional lender, make sure your financing is lined up.

Here are the pros as i see it: easy (no purchase necessary, you know the property), likely prop 13 property tax discount, possibly below current rate loan.  

I'm a new real estate investor just looking to get more knowledge on how FHA loans work.

I have found some information that might be helpful John.There are government backed programs like Fannie Mae Homestyle Renovation Loan and Freddie Mac Home Possible Renovation Loan, in addition to the FHA 203k loan. 

It recently dawned on me the idea of a non military affiliated individual assuming a VA loan, would this individual be able to then also gain the benefit of using an IRRRL since they have now acquired a VA loan through assumption?

If the lender is licensed in the state you're buying in, then they can do the loan.

We currently own 13 rental properties and have paid off all loans/mortgages including our primary residence. 

You should speak with a CPA and a tax attorney to be safe.Regarding your thoughts about 1/3 equal splits - sounds good until you check out the cost of getting a DSR rehab loan or borrowing hard money.