Can I have an appraiser check it out before the bank?

There will probably need to be a survey and an appraisal.

Taxes are accurate from appraisal website.

Obtaining a note from a private lender may be difficult, so my question is would a conventional loan be an alternative (assuming it would appraise) to settle the balance with the HML ($272,000)?

Seems like something you should hold on to at this point, even if you don't refinance the entire difference between the current note and what you believe it would appraise for.

It's a single close loan and avoids having to refinance, order another appraisal, pay closing costs twice, yada yada.Bottom line unless you have unlimited funds, your strategy HAS to allow you to get your money back or else you will run out and have to wait a LONG time before you can buy another property.In case you're curious my previous job was working in Consulting making a high six-figure a year salary. 

But this will be determined by the appraiser and you will need to qualify as it would be owner occupied property. 

I actually just received the appraisal report. 

No origination fee but would be responsible for title fees as well as appraisal fee.

The property management company was the party that arranged for certain repairs to be completed per the VA appraisal.