So I decided to work with logs instead. I went quite a way with it and the common physics relations transformed straight into common economic relations. Plus it provided a number of insights which made me, for myself, redefine some terms. Now, in my head, price is a number determined by the market and trades. Two things have the same price if they are traded for one another.
Value is a number determined in the absence of a market.
Two things have the same value if you would be unable to choose which one to discard if you had to discard one. Now price and value are a pair. In the regular world, the price is somewhat uncertain and so is the value. But the uncertainty in measurement of the two together is related. As I said, I think what I have found opens up things to think about which are beyond anything I have ever heard discussed.