This sounds like a classic negative feedback oscillation. You sense the
signal is too large, so you send a signal to kill the gain, and then
you sense the signal is too small, so you send a signal to increase the
gain.

Having different attack and release time means you have two different
time constants My guess is the quick attack leads to the instability,
since it is the lesser damped system. If this is true, then you should
concentrate on the attack time, i.e find how slow it has to be for the
sytem to be stable.

Of course this is really had to do without seeing the circuitry in
action.

I agree with you and slowing the attack is the only way that I have
been able to approach stable operation with a fast release. But 20ms or
longer attack runs counter to what I understand to be the objective -
an attack speed of less than 13 ms and ideally about 1 ms. So, unless I
have this wrong, how do other receivers accomplish similar speeds
without self-oscillation?

The way my circuit operates (I think) is as follows (I'd be happy to
send a schematic to anyone who is interested) :
a) assume an impulse of signal of duration very much longer than the
attack time
b) the rectified signal is filtered of RF by a series-parallel R-C
attack network whose adjustable output feeds an emitter follower
c) the emitter follower pumps current as a low resistance source into
the release R-C network so the attack is not greatly slowed - its
output feeds the AGC driver amp
d) at some point, equilibrium should be reached - the current flow
through the release resistor and AGC driver base should equal the flow
though the emitter follower - but maybe the emitter follower pinches
off and that could be a cause of instability?
e) the signal drops, the attack network discharges at attack speed and
shuts off the emitter follower, so the release capacitor discharges
through its parallel R at release speed, the voltage to the AGC driver
falls so the AGC bias rises at roughly release speed to increase RF/IF
gain.

Having written that out, I have an idea or two I will try.

Tom