I think you have accurately identified the problem, but it looks like
the only solution i have is the one you have tried.


http://www.epanorama.net/documents/g...oop/index.html

here is a good explanination of ground loops and ways to fix

according to this site, ground loops could cause damage to the system.

according to the site "A ground loop in the power or video signal
occurs when some components in the same system are receiving its power
from a different ground than other components, or the ground potential
between two pieces of equipment is not identical"

my personal suggestions: (not based on experience, only on information
from the above site.)

OBJECTIVE: Eliminate ground loops
Ground loops are caused by the resistance between the grounds of two
electrical items not equaling zero. So, how do you make the resistance
between the two grounds equal zero?

Solution.
1 move the grounds closer together(inverter ground closer to wherever
the audio ground). Less distance = less resistance. Methods for
execution are : Try hardwiring the inverter to your car instead of
using the cigarett adapter (remember thicker wire means less
resistance, but at some point the effects of larger wire become
insignificant. There are charts that give the resistance of a certain
gauge wire over a specified distance. the relationships are also not
linear.).

this may just be a waste of time.

you might want to barrow somone else's inverter and test the effects as
well. i am not implying that there is anything wrong with the
inverter, but different circuitry might have a different effect on the
system.