You are right that the correct definition of "equity" is the home's market value less debt secured by the home. But again, unless you actually put the home on the market and solicit bids, how are you going to determine market value? You are worried that a home's appraised value "could be more or less than market value." Yes, that's right, but the same holds true for any of the other methods of determining market value that you mention: Zillow, newspaper listings of home sales, consultation with a real estate agent, or anything else.
In my first response to you I said that an appraisal specifically geared towards determining market value (not for mortgage purposes, or refinancing, or a tax appeal, or "drive-by") could be done. In my opinion, while certainly not the only way to determine market value, that would give the most accurate result (and also be the most expensive). Once more: unless you actually market the home and receive bids, anything you do to try and determine market value will just be an educated guess, with some methods being more reliable than others.