So far the results have been very promising. In order to get a precise approximation of the original analog meter, I wrote the code in a way that instead of just setting a character to a black box, I defined 5 custom characters on the HD44780 display which allow me to display the meter in a very fine resolution (80 pixels instead of 16). This works really well. As the original meter did not have markings either, I felt this is a more than adequate replacement.
The frequency display works nicely too. I made the mistake first to believe it would be sufficient to feed the output frequency directly into the prescaler clock. This works but when in balance (50||50), the bridge draws too much current to keep the voltage high enough for the counter to work. Same as in Lucs original design I then added a buffer stage.
In general, the design works but requires the operator to understand what he is measuring since the square wave that is used for measurement produces "ghost resonances" at harmonic frequencies. Those would be at different impedances though so they can be identified.