Big 4/0 cables
to the panel? That's very unusual. Is the inverter also powered from the panel? That would be the only reason I can think of in using such heavy cables to the distribution panel, unless the batteries are 50' away!
Still, it's a good idea to power the radio directly from the house batteries, using AWG6 cable up to 20' one-way runs, or AWG4 cable if longer. There should be a 30 amp fuse in both the positive and the negative cables, located close to the batteries.
One important reason for going direct to the house batteries is that they act as giant capacitors, helping to filter out conducted RFI in both directions (from the transmitter to other instruments, and from other equipment
onboard back to the radio).
The note about not grounding your radio directly is a good one, despite the instructions you'll find in many manuals
. This can cause ground loops of RF (which is AC) and be troublesome. Better not to ground the radio.
Try to keep the coax between the radio and the tuner away from other wiring
if possible. Also, I've found that using RG-214 double-shielded coax is helpful in reducing RFI. You might also try some heavy ferrites and, possibly, an isolator such as the one made by Radio Works installed in the coax near the tuner.
Finally, it's best not to connect the tuner ground to your boat's DC ground system, or bonding system, or lightning
protection system. A short run from the tuner ground to the nearest bronze thru-hull -- which is not otherwise connected to any grounding system -- would be sufficient.
Also, some have found that the use of the KISS-SSB radial grounding system works wonders for eliminating RFI in instrumentation. The Nordhaven folks have adopted this system, and I've found it works well.