The Vcc part is right. And yes, this will tick up then down all day long when no adjustment is needed. If the change in gain is small enough and slow enough, you won't notice it. Human ears aren't all that accurate. Be sure not to let it make decisions at audio frequencies. That is, keep the 555 running slower than 20 Hz. A lot slower if you can.
There is a thing called a transconductance amp..single chip like an op-amp. Its gain is controlled by how much current is flowing through a circuit in the chip so it's easier to adjust. Too much loudness? Reduce the multiplier current. Completely analog. No incrementing, no timer needed. Look 'em up and read all about it. See if that's what you need.