The diode rings have the advantage that they will work at substantial signal levels, so are often used for frontend receiver mixers, as they are pretty well immune to cross modulation. 1496 are better balanced, and probably better for generating SSB, but not so good for a receiver frontend mixer.
You posted a circuit a while back using just two diodes, and a preset to adjust the balance - have you tried making one like that?.
If it's of any interest?, my long ago receiver used a dual-gate mosfet front end, with delayed AGC applied to the second gate. It was fed from a tuned pre-scaler, with a manual attenuator on the front to prevent overload and crossmod. The mixer was another dual-gate mosfet, and the oscillator used bi-polar transistors. The IF used CA-something or other IC's (they've been mentioned somewhere in these threads, can't remember the number - I've still got a couple left somewhere?), feeding a 1496 product detector. I used a 9MHz crystal filter, with matching upper and lower sideband crystals, I used two separate oscillators, and switched power between them, making the switch non-critical, and outside the screened box.
Like I've mentioned previously, my original intention was to make a transceiver from it, but I never passed my morse test, so never bothered. I've still got the Plessy SL6-something IC I bought for the mike preamp, which did all the processing in a single IC.
