So, I’m going to use the extra money from my loan to cover closing and repair costs (if necessary).

I didn't realize I needed to get a permit from the town. 

Will it be life changing probably not but it will definitely help you save faster, give you extra discretionary spending and if you occupy it while renting out the other half (2 family situation) can give you a HUGE advantage allowing your tenant to pay 1/2 or even 3/4 of your mortgage payment (this is how I got started) over time this can really snowball into something big if you are diligent, patient and choose to keep going...regards,Chris  

Anyways - I have estimated the rehab to cost around 20K-22K when all said and done so I was wondering, what is the best way to finance that extra, lets say, 12K?

Sometimes investment property appraisals tack on an extra $100 or so for the property’s rental income estimation if they are going to count the property’s rental income towards helping you qualify for the loan. 

Well, then you made good extra money and didn't have to deal with uncertainty while you were long-distance. 

Between due diligence, rezoning (if applicable), site plan approval, construction drawing approval, offsite easements, permits, etc. it is a lengthy and expensive proposition.

Andrew, if you are also looking for extra capital for a down payment and have some funds in your TSP, I just learned that you can take a loan out from both your Contributions AND Earnings (from either/both your Traditional and Roth). 

My tenants have been in my properties a long time so I have been able to bank that money as extra profit.

I received an extra copy that I am willing to give away to anyone in the BiggerPockets community.