The commingling funds portion I would get a lawyers opinion.

I pretty much may have to go the untraditional way to get funding, I do not want to, the rates are explosive!

Should I invest my own money into the property before I own it just to get VA funding?

You certainly would want some sort of slush fund for expensive stuff that could go wrong up front but assuming you budget for it, the rental income should pay for the repairs over time once reserves are built up.  

Can anyone recommend any private funds that specialize in SS for accredited investors? 

Showing within 24-hours after accepted offer with proof of funds or lenders pre-approval"...something to that effect...just depends on your market and state requirements.

If you do not budget at least 5% for the tenant that loses their job or decides to stay and not pay, then where would you get your funds from? 

Alternatively, you can try to get a private money loan or ask the seller to finance a portion to reduce the down payment, but typically equity is the preferred method when you need funds for a down payment.

Therefore, we will be liquidating shares of our Vanguard index funds (held in a general brokerage account) to make the down payment. 

@Amadeus Hladun where do you intend to get the renovation funds and do you actually have the skills to estimate correctly and execute a fairly major rehab ??