It might be easier than that. Are the bass lines totally missing or are they just very weak? If you can capture a recording using vintage equipment and the placing of it, you can get the system response. Run the original recordings through an inversion of the response and you should get really close. Another possible method is to find the transform between an identical modern recording of the song and use the difference between the two recordings to make your transform.

So the idea would be to reconstruct the low frequency components from whatever upper harmonics are left in the recording? If you know the instruments and positioning of the recording device and something of its(the instruments, recorder, environment, etc.) characteristics, it might be possible to solve that using classic methods. There would be huge numbers of parameters, it is an interesting thought. Is there a large easily/freely available corpus of those recordings?

To do this, I think you are right that you would need to 'downgrade' modern recordings to sound old so that you have both sides of the training data covered.

This would be a cool project to work on. Ideally you would buy some vintage gear and then run the audio through both, but that would be very expensive. You could may be find some vst emulations though and get decent results.