John,
You have a bunch of possibilities here. First off, radio? Who listens to the radio in their 6? That aside, a whine might indicate bad brushes and/or cruddy connections. Have you taken down your alt plug lately and looked at it. I routinely (annually) disconnect all electrical connections and scrape them for better conduction, especially those many bullet connectors. A little dielectric grease can't hurt. Are you using "R" type (resistor) spark plugs? Can't hurt. All brands offer resistor plugs, in fact it is hard to find non-resistor types. If you are interested, and this is not a comeon, the alternator from my 73 TR6 (correct one for that year) was rebuilt by TRF about 10K miles ago. I went with a Delco and have no use for the Lucas unit. It worked fine when I took it out last year. New rebuilt is about $110.00, I will sell mine for 50 bucks and that includes shipping. If you don't think it is worth it, I will offer a money-back guarantee. It is in perfect order.
Keep on pluggin....
Bill