I like the poptronix solution
Some quite observations:
1) the rail spliter, built around a TL0xx, is surely unable to hold the rail steady, and an oxymoron given the current amplifier used Q2.
2) the current amplifier Q2 is not needed, as its load is on the tone of 500ohm. I would get rid of Q2 and put the bridge on the emitter; alternatively, get rid of the IC1-a and IC1b, and use a 555 as the oscillator and go single rail;
3) the differential amplifier IC1-c requires matching resistors. Given the use of a meter as the read-out instrument, I would combine IC1-c and IC1-d into a true difference amplifier (aka the input stage of an instrumentation amplifier) setting gain with 1 resistor.
4) the rail splitter is required in this design as the input signal could potentially go very close to the ground. One way to solve that issue is to use padding on the bridge, or to use an amplifier that is (at least) r2r to the negative rail (ie, an opamp with pnp input stage).
This whole thing can be built around a 555 + a (dual) opamp (or a single instrumentation amp).
I don't think I have the necessary opamps
Many opamps or even comparators will do. The lowly ne5532 would be more than enough here.