It sounds like a technique I remember calling "controlled carrier". The
carrier power was reduced when you weren't talking, then was increased
with the audio in an AGC-like manner. Sounded a little weird, but not
badly distorted. The objective was to reduce the average dissipation of
the final stage, so smaller tubes and a lighter duty power supply could
be used.

But I don't see why you'd use a method like this with a low power
transmitter, since it's trivial to make one that easily handles the
power requirements of standard AM. So I don't really think that's what
is meant by "swing". I'd bet good money that whatever "swing" is, it
doesn't improve quality or signal strength, and very likely introduces
distortion that causes splatter. If the transmitter was designed for
100% modulation of a 4 watt carrier, and you reduce the carrier without
a proportional reduction of the audio, you'll be overmodulating and
consequently distorting and splattering.

What are the supposed benefits of this "swing"?

Roy Lewallen, W7EL