Yes, a small mandatory proportional fee should help.
I think high volume should be interpreted as a symptom of inflation, not deflation, so the network would act the opposite way you describe.
With high volume, the demurrage would decrease but the reward would decrease even more (making dM negative).
Just exploring ideas...
Our equation for change in price:
%ΔP = %ΔM + %ΔV – %ΔQ
Our goal in math: find a function f(%ΔV), such that if we set %ΔM = f(%ΔV), then E[(%ΔP)] = 0
Our goal in English: find a money supply rule that minimizes expected price changes given what we observe about velocity
One obvious f(%ΔV) to choose is %ΔM = -%ΔV, this takes velocity out of the price change equation. However, if %ΔV and %ΔQ are correlated, then this is not a good rule.
The best rule to pick is f(%ΔV) = E[ -%ΔV + %ΔQ | %ΔV ]. However, we have no idea what E[ -%ΔV + %ΔQ | %ΔV ] is and there is no obvious way of estimating it.
In short, we are up shit creek.
We control M directly: dM = R (Reward) - D (demurrage rate)
But we control V only indirectly.
V rises with D and dM (and decreases when they decrease)
With dM = 0, dV > 0 => dP > 0
The functions we need to adjust are R = f(dV) and D = g(dV)
I'll keep on thinking about this. I didn't though the implications of knowing V because I though we could not know it.