Some quick suggestions, based on a project I did that looks quite similar to yours but worked quite differently.
Your output is subject to the diodes non linearity, which can be an issue when high ear shows up. You can solve that but putting the diodes in the feedback loop.
The whole design can be made single rail, siify the design.
You may pick an ohm meter with the right center resistance marking - your meter has reciprocal reading, like most ohm meters.
The oscillator can be made to much like a sin oscillator by adding a capacitor.
For insensitive meters ( over 1ma full scale), a buffer, like emitter follower can be used.
Like yous, my meter is also designed around a dual opamp: one opamp functions like an oscillator, almost identical to yours.
My second stage is a non-inverting amp, with the dut from the inverting end to ground, and the diodes plus the meter in the feedback loop.
It has excellent range and calibrates very nicely to theoretical levels, as any non linearity is handled by the opamp.
Very compact. As a matter of fact, I build one for a friend Manhattan style on a ne5532.
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