OK, I've seen a number of useful replies to my question. I will
test whether the empeg case is grounded with the RCA cables off

Yes it was.

try powering the empeg direct from the battery

No change whatsoever.

try grounding the empeg direct to the chassis

No change whatsoever.

try a 10A power filter I just bought

Yes, that's it! It's 100% gone! The power filter is from Freitag Elektronik.
I bought it for € 9 at my local Media Markt store.

try combinations of the above

Not necessary. It's the power filter that does the job.

Tony Fabris wrote:
No, you will still use the ignition-switched wire for the switched power lead.
Only the constant-power wire should come straight from the battery.

For me this translated to: only the constant-power wire should be connected to the power filter.
Oddly enough, disconnecting the the constant-power wire while the Empeg is playing will not stop the player.
So the Empeg can draw its power from the switched-power wire too, which, as it appears, is less perceptive to noise.