The largest clue you've provided is: I also get a steady 15% modulation. I think its got a humm when keyed like that. Help?
The electrolytic filter capacitors are gone. Well, functionally "gone". Odds are that there is a visible "zit", an outward puncture on the rubber end-cap of one (or more) of them.They're only supposed to be good for 10 to 20 years in the first place. If the filters in your unit are original, that makes them closer to 30 years old.
Never have found a diagram for that amplifier, so I don't know what they used. usually two 450-Volt parts in series. Some manufacturers back in those days (D&A,Varmint) used a series string of three 350-Volt parts.
Don't even know whether it uses a low-voltage 12-Volt relay and a transistor to activate it, or the older 110-Volt DC relay with a tube to sense the RF and key the relay.
Either way, it sounds like you have gotten your "money's worth" out of the electrolytic caps in this unit, ESPECIALLY if they are original. As a rule the only rational way to return a unit like this to regular service is to replace them ALL. Scorched earth, no exceptions, for any electrolytic cap that looks over 20 years old.
If there is a separate bleeder resistor in parallel with each of the H.V. electrolytics, they are probably old, cheap carbon-composition type resistors. They don't age gracefully either, and should be replaced along with the filter caps. If the resistance value of an old bleeder has changed too much, it could cause excess DC voltage to be put across one of the filters. The bleeders are cheap insurance, compared to the cost of blowing out a new filter cap.
And if it has just one bleeder, with NO separate resistor in parallel with each series-connected filter, they need to be added. We use 240k 2 Watt, but there is latitude to this value. Smaller resistance calls for a larger wattage rating. Don't recommend using a resistance any higher than about 500k. Just so that each of the bleeders placed across filters in series are the SAME value. That's part of their function, to equally divide the high voltage two ways, three ways, however it's arranged. You don't want one electrolytic to have more than its 'share' of the HV placed across it, or its breakdown rating could be exceeded, causing it to fail prematurely.
73