The operative word in two of the above is likely 'ground(s)'. Coax that's properly terminated and grounded at both ends should not radiate any RF energy along it's length. Unless the antenna is inside the cockpit, its radiated energy shouldn't affect instruments inside the plane. One way to check for a radiated RF problem is to ask a HAM operator to borrow a 'dummy load'. Disconnect your antenna lead and hook it to the radio's output. See if the manifold gauge still acts wonky when transmitting into the dummy load.
Ground paths for both the radio and other instruments, etc can cause 'issues', though. Was the plane wired with a 'forest of tabs' single ground point near the battery, or isolated from the airframe with a heavy ground run back to the battery?
The compass problem could easily be real estate (location location location). Any power wire with DC current flowing through it has a fairly strong magnetic field around (but fairly close) to it. I know; 'fairly close' isn't quantified, but look at where your power wire bundles are located in relation to the compass. Also look for any iron/steel structure that's near both the wires and the compass, since the magnetic field around the wire can turn nearby iron/steel into a magnet.