A battery is a very stiff supply and such a low impedance that it acts as a capacitor would do smoothing out fluctuations.
Is any part of your wiring to the stereo shared by the lighting circuit or does any of it run side by side?
Well there is one strange thing going on.
When I initially connected the stereo via its own fused lead to the leisure battery I opted to leave it connected to its original earth i.e. I did not run a cable from setreo earth to battery earth.
I thought I would try putting that right. So I ran a 15a lead from stereo earth to battery earth and no change. I then (accidentally) knocked the earth lead from the battery and the stereo still worked! By my understanding this must mean it is earthing somewhere else. Not via the aerial since it worked with this disconnected also.
The only conncections to the stereo now are an aerial, a 12v lead from leisure battery, and 4x 2 speaker cables.
It does get better with bass low definately. I did run a 15a power lead from the battery to the stereo, but same problem. Only non-standard thing I am doing is putting one input into both the strero continuous/ignition circuits via a push-splice.
And I know this is no help but for one minute while I was messing around things seemed o.k.! I don't know why!!
The lighting/charging/stereo lead all leave the positive pole of one of the two batteries, earth from the negative of the other, as suggested by cleverer folk than me on here ;-)
p.s. One other thing I have changed come to think of it: I changed a halogen bulb to a l.e.d. The halogen was running off 10w, the l.e.d. off 1.3w.