Ring Modulation: Differences Analog to Digital

I am rebuilding old compositions from notes of the composers digitally and ran into a problem that I could not find anyone talking about through google: Composers have built complex tones with additive synthesis that they would then ring modulate together. These complex tones had partials at different volumes fade in at different times.

Now, when ring modulating two tones at volumes lower than 0dBFS their resulting sidebands result in the multiplication (in amplitude - or sum in dB) of the volume of both the carrier and modulator. Hence, a carrier at -20dBFS and a modulator at -20dBFS will result in sidebands at -40dBFS. This is obvious one thinks of the multiplication done for ring modulation, as we all learned it in school. The thing is, at -40dBFS you cannot hear bearly nothing anymore, and I doubt the composers aimed for such a result.

The actual circuit of the ring modulator, as I recall, does not simply multiply the two signals together. I does create the same sum and difference tones, but I think it must have done something different with the amplitude of the result.

Therefore, my question two the community: does anyone know of a better way to do ring modulation that resembles the original analog circuit? One that does not "tamper" with the amplitudes of the resulting sidebands?

Cheers!