That said, the size and condition of the facility as well as the size and health of the market will come into play. 

They come with more requirements and strict livable conditions to be approved.

Is it possible to contact appraisal people (or someone else; no idea who) and ask for a "soft appraisal" based on images and current known conditions, but without them going to the property?

Property: TriplexLayout: Main level = (1 unit) 2 bed / 1.5 bath             Upper level = (2 units) 1 bed / 1 bath Condition: Both upper units are messy (tenants) and rented under market value.

Depends on neighborhood class, condition, etc.

Assuming everyone is being friendly and you can do a walkthrough and the home is in the same condition meaning nothing to deduct from the exsisting deposit you can simply do as you suggested, refund the exsisting and collect new deposit and start over with a fresh lease. 

If the appraiser identifies anything in the property that would require work to be done to bring the property to 'move-in ready' condition, they will call that out in the report, and those items will need to be addressed prior to closing.

While I don't have a reason to doubt what the tenant is telling me about their medical condition, getting the run around for four weeks doesn't breed confidence. 

It was in AWFUL condition, but the bank gave us money to repair and update it. 

This price seems high to me, considering the work that needs to be done plus I have looked at other duplexes in the area that have sold in the last two years and they are selling at about the same price but are in move in ready condition.