I think it should appraise for $400,000 at that time.

I think it appraises much higher. 

Any tips on what I should be considering when trying to understand how it would be appraised for re-fi?

Be sure to go at least 10% on Cap Ex Reserves since, as you said, there is a lot of deferred maintenance.Also, be sure you get an accurate, 3rd party appraisal that supports the sale price. 

@ IMO who cares about up or down 10 - 20% , ( But I do always buy much lower then appraisal ) buy rentals.

Appraised at $425k, new mortgage at $2330 at 4.35% currently owe $305K now.

The reports are 40-90 pages long and go through the entire house in great detail.Get an appraisal.

@Jacob Scholes the appraiser will do a projected rents schedule and whatever you submit as projected rent - as long as they appraiser justifies that it is within reasonable range is used.

Sounds like you have already had some negotiations so at this point keep it unemotional by presenting your offer from the perspective of an appraiser.

I have almost $1,500 between appraisals and extensions.