Well ive tried to follow what you rote,
But you make it hard work.
Both sides of the thermocouple cannot be grounded,
or it would not work.
I suspect that you mean one side is connected to the
casing of the thermocouple in such a way that when you
bolt it in, the body of the thermocouple housing will
be fixed to the head metal-to-metal, and that it is
made in some way that prevents you from disconnecting
it without damage.
I also suspect that when you say the other side is
grounded also, you simply mean that it is a very very
low resistance. This is normal, a thermocouple is a
very low resistance.
But the wire coming away from the thermocouple should
not be grounded. You should read a very low voltage
from it, to ground.
Now i am not clear where you are putting the probes
of your meter when you say:
"the potential from the head to the batt(-)"
You are dealing with very small voltages and you have
to measure in the right places.
I have attached a small pic, you may be aware that
these places are potential problems, but you may not
be aware that wherever dis-similar metals are touching
there will be a potential difference.
This normally does not matter, as such voltages are
quite small.
However where thermocouples are involved these voltages
can be significant.
They are not just caused by poor connections, that may
require cleaning, these voltages are because of dis-
similar metals coming into contact.
Also, you mention there are spurious voltages getting
into the signal area with the engine running. These i
guess are from currents flowing along 'shared earths'
You say you have tried with the amplifier earthed at
the thermocouple, but of course the battery ground
would go through several other junctions to reach the
case of the thermocouple.
I think your best answer would be to modify the thermo-
couple into a two wire unit with no ground.
I think your problems now are with earth/ground currents
interfering with the signal, such currents when the unit
is running could be from charging, or just the ignition,
or maybe injectors, most units share the common ground
connection, and i don't see how you could easily isolate
the thermocouple signal from other currents sharing the
Batt(-) terminal.
It might be possible to run a (slightly) lower voltage
supply from the 12v rail, with its own earth at the
thermocouple casing, if you were willing to make an
additional connection at the thermocouple.
I will follow up with a possible diagram.
Best of luck with it, John