If you could find a duplex property (or a single family house that could be turned into a duplex--check any HOA restrictions first), or a "fixer upper" to live in, that could be a better use of the equity you have in the rental house.If you run the numbers and decide it makes sense to sell the rental house (check with your accountant, figure out closing costs to selling and buying) then you'll possibly have more money to put towards a primary residence.You may want to check the neighborhoods that fall in the school district you want to stay in and look in "under appreciated" areas...maybe not the A class neighborhoods, but ones that have potential of becoming "improved".While I understand your desire to stay in a particular school district, it's not the end of the world to consider other districts if they will allow you to build real estate/family wealth that will put your entire family tree in a better position."

Well worth the money.

I am re-reading 'The book on Rental Property Investing' by Brandon Turner then going to re-read 'The Book on Investing In Real Estate with No (and Low) Money down' by Brandon Turner and 'Buy, Rehab, Rent, Refinance, Repeat' by David Greene. 

if so, what would be the best way to get the money to fund this without having to do partnerships?

I’m currently have all my money in a live in flip but see opportunities all the time.

We spent money on the inspector, the appraiser, and the lawyer.

I considered ordering the lender's inspection/appraisal, but this wasn't an option because the water and electricity are currently turned off, and HUD won't turn them back on until I have submitted earnest money of $2,000.

It's so easy that you really don't need anyone, but an escrow company involved in the transaction, so you would be saving lots of money. 

When you say you are paying them - is this money going directly to them or into an escrow account?

I have purchased a set of 4 properties in Salem NJ and need to refinance them all to pay off private money lenders.