However, I would definitely want to see the loan handled by a "local" lender - not one of those online VA loan companies.

Any other ideas to help not pay a mortgage and rent for 3 months?

If you walk out your front door and talk to your neighbors about finance - they will talk about the interest rate on their mortgage, their 401k and T-Bills. 

Since the sellers are opposed to seller financing, consider exploring alternative financing options such as traditional bank loans, private lenders, or hard money lenders.

Thus, the investment grows like it's sitting in a roth 401k/IRA       Then when you die, your heir gets a step-up in basis, thus eliminating all the prior capital gains over decades, but only up to 13.6 mil this year :(              Debt Funds (like mortgage note investing) can also be very lucrative but I don't know/understand the tax savings/issues in that class yet, still learning :)              Equity REIT investing can give you great siloed real estate exposure in 11 major asset class sub-types, but don't offer the direct tax benefits as direct RE ownership does above, as the REIT gets those benefits when it transacts and as a corporation passes those benefits secondarily/indirectly onwards to us investors as high dividends and gradual stock price appreciation.

I'm a lender and attorney in the state of illinois, so while this is not 

The most obvious is that you will be able to offset your mortgage with renting out a few rooms.

You would need to consult with a (local) lender to see what is available to you for that property, but I am assuming 20-30%.You would likely have 2 options with that property - 3 2 bedroom unit listings, or 1 6 bedroom listing. 

and to house hack you'll need to get an agent and a lender and then... go look at a bunch of properties. and it might take MONTHS. and you might have to look at dozens of properties.

A knowledgeable VA lender can provide guidance tailored to your unique circumstances.