you say "Ignition whine"... is that really what it is? Does it follow engine speed (i.e., as you speed up the ENGINE, does the pitch of the whine change? If the engine is off, is it whineless?
If so, that's often a sign of a bad alternator. The car alternators (how portable this is to the LT, can't say for sure) I've worked with will typically have three sets of windings/diodes, and if one of the diodes or windings is bad, you will get a whine through the audio system, even though the alternator will still put out enough juice to keep the car running indefinitely (though you may have problems when loading it up -- idle, lights on, heated grips, heated seat ... and things might get unhappy quickly should another diode or winding fail)
I'd suggest starting by figuring out where the whine is coming from -- you have two choices, really: through the power or through the the air. Disconnect your sat radio's power from the bike, and power it from "something else" -- preferably a battery. Make sure you ground your "something else" to the negative terminal on the battery of the bike. If that eliminates the whine, it is coming through the power system...start looking at your alternator.
If you still get the whine, it is probably coming "through the air", probably due to something routing near spark wires, ignition computer or similar. At that point, the ferrite beads (not magnets) tvguy mentioned above might help, though rerouting would be my preference. And yes, you can scavenge these things off various cords with big mysterious blocks near the ends. If you hunt, you can get two-piece cores which can be clipped around existing wires without any disassembly. They work by basically turning your wire into an inductor which will actively block higher frequencies. You might be already seeing a problem here -- you have an audible frequency you are trying to block, which is fine if it is riding on a power wire, but if it is riding on an audio cable, you probably don't want to chop out those frequencies.