I saw an article on Am modulating by altering the axial magnetic field, but my brain cannot process such complicated things. I have a different idea.
Why not use a wave guide to couple CW energy into an antenna array that has elements electronically switched at an audio (or whatever) rate such that the antenna pattern moves? The load on the magnetron remains constant, only the directivity of the array is altered. Would that not simulate AM modulation in a given direction??? Make the pattern of an electronically steerable antenna rotate/shift at a speed proportional to the modulating signal.
If efficiency is not a concern, just throw away half the power and put a few circulators in line with dummy loads to deal with reflections, and then electronically de-tune a fixed-direction beam.
Rotational Modulation, Patent pending lol.