In LTspice, I compared a self-oscillating cross-coupled pair mixer with a separate transistor mixer fed by a separate LO. The conclusion is that in my tests, the separate transistor mixer has superior conversion gain.
The idea for the self-oscillating mixer was described in another post by @Sean O'Connor here: https://www.theradioboard.org/forum/main/comment/57b6d337-3027-4e59-bf1e-7500a2278061?postId=65b3862e1b35030010821722
Basically it was the cross coupled oscillator, with the one free base connected to a ferrite rod antenna for preselection. And the free collector connected to an IF transformer.
I would design it slightly different today with a Seiler oscillator as the (oscillating) current source to the differential pair in place of the single resistor and then just a ferrite rod antenna connected to the base of one transistor and the IF transformer to the collector of the other transistor.
That results in a very stable, low phase noise oscillator as one input to an active multiplier (mixer) circuit and the signal from the ferrite rod antenna as the other multipler input.
Here are my results. First, the 2 circuits being compared were modeled in LTspice.
The self-oscillating mixer (RF1, LO1, IF1) is at the top, while the separated LO-mixer combination(RF2, LO2, IF2) is at the bottom.
A transient analysis was performed to determine the actual oscillation frequency of each LO.
Then an AC analysis (frequency sweep) was determined to confirm the resonant frequency of each IF tank. Both IF tanks were resonant at the same frequency.
Knowing the LO frequency and the IF frequency, we know that then the input RF frequency should be equal to LO - IF, so that after conversion the RF signal gets converted to the IF frequency.
The resonant frequency of each RF tank is confirmed to be adjusted properly (RF1 = LO1 - IF2, and RF2 = LO2 - IF2) by again performing a frequency sweep across the RF tanks.
A 1 microvolt peak amplitude-modulated signal was fed into each RF tank at the proper RF frequency, and the output at each IF tank was graphed.
Already in the above graph, we can see that the output from the separated LO-mixer combination (the bottom blue trace) has a noticeable 1.8-MHz wiggle on the upper and lower edges, corresponding to the converted input AM signal. On the other hand, the self-oscillating mixer's output (the top green trace) seems to have no visually apparent trace of the IF at this magnification level. This already indicates that the separate LO-mixer has higher IF output.
Zooming in, we can see that in the arbitrarily-chosen time window, self-oscillating mixer's output (green trace) -- the height of the "wiggle" on top of the LO signal -- varies from about 654.372 mV to about 654.380 mV, for a difference of about 0.008 mV or 8 uV.
For the separate LO-mixer combination (blue trace), the mixer output varies from about 651.880 mV to about 651.980 mV, for a difference of about 0.100 mV, or 100 uV.
So in this test scenario, the separate LO-mixer combination is giving vastly higher output than the self-oscillating mixer.
As a quick test to try to improve the self-oscillating mixer, I did try another experiment where I reduced the base current on the left transistor in the cross-coupled pair (biasing the base not directly to Vcc, but instead through a 100k resistor to Vcc, grounded at RF by 100 nF), but this made no significant difference in the self-oscillating mixer's output.
The results are clear enough to me that I'm not going to try to build the self-oscillating variant and will stick with the separate LO-mixer combination.