Component selection:
1) most parts are non-critical, other than the few listed below.
2) opamp - I used ne5532 and tried others. ne5532 was selected for its abundance and reasonably fast speed - the opamp needs to swing at least 1v/us.
3) R4: needs to be the center resistance of your meter, to minimize the amount of math needed.
4) C5: determines the frequency of the oscillator.
5) R1/R2: need to attenuate so that the detector's output swing is around 1v. Too high of a swing will require higher supply voltage or lead to clipping / inaccurate reading. I have found that the output from the oscillator can deviate considerably from simulation so you will need to play with R1/R2's values - it is not impossible that R1 goes to 330k or even 470k, vs. R2 of 1k.
6) D3/D4/R11/R12: D3/D4 are schottky diodes (I used bat54s. Germanium diodes work too). R11/R12 can be replaced with schottky diodes too. Silicone diodes can be used if the supply is 9v or more.
7) DUT protection: you can put a pair of diodes on DUT in case it is charged. Not drawn here.
lower voltage operation: I didn't try this but if you go with a r2r (output only) opamp, you can get the meter to work at 3.3v or more, making it possible to use phone batteries here.
9) current consumption is very low, at 4ma.