Buying with VA loan, IRRRL, and Conventional in 3 months?

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Hi, I'm an active duty military, separating soon, and new to real estate.

Can you someone at my scenario and see if it would work out? 

Buy a house for $200K using VA loan with an interest rate of 4.2%.

Live in it for 1 to 3 months, and use IRRRL to get rid of occupancy requirement (IRRRL rate is 3.999% right now)

Turn the house into a rental property.

And lastly, use the VA entitlement leftover or the conventional loan to buy my primary home?

I'm guessing all these could take place in less than three months (I already found my tenant: my parents).

However, I saw that the banks usually want a 'history of mortgage payment' for filing IRRRL, but I also read that I could shop around and eventually find one that would work with me.

Any ideas, feedback? Thank you!