I set up a simulation using a very similar design to yours with some minor modifications.The first circuit didn't get its fair day in court. I put its output through my recently-made IF amplifier and I am only now discovering it to be a source of distortion. I'll have to fix it.
I'll play with the first circuit today after my chores and see what it can do. I think it should actually be a high fidelity circuit. Have you noticed that both circuits are purely passive? And, except for the LC tank at the output of the second one, they're not tuned. This is an advantage for me since I intend to put an AM modulator in its own aluminum box and use it for experiments. I'm waiting for a couple ICs in the mail so I can breadboard them and then pick the best modulator for the box.
The trick is (as suggested) to correctly filter the output. I used a PI section high pass matching filter between the output transistor collector and a 1KΩ load resistance. One can match to a range of load resistances.
The resulting AM was good quality with some very minor distortion. This showed up as low level residual sidebands in the frequency spectrum.
Of course adding the matching network limits the operation to a small frequency band - something you seem to be wanting to avoid.
One doesn't need to drive the signals into distortion - the differential pair gain modulation effect works quite well in the linear region.
Another approach, which seems to have promise, is to replace the output transistor collector resistor with a RF transformer with a suitably loaded secondary. This would give a potentially greater bandwidth as the transformer needs only to reject the low frequency modulation signal component in the composite waveform. So this might fit with your requirement for an "untuned" device.
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