The problem is not that Q519 and Q520 "can't handle" the current. They are being forced to generate about 2.6 watts (total) in heat energy, and I have to assume that the heatsink can't dissipate this energy, because it's getting a lot hotter than it should.
The reason why Q519 and Q520 are generating so much heat seems to be that the tone control board is drawing too much current. It is drawing 42 mA. But I can't be sure how much it is supposed to draw. That information is not shown on the diagram. I believe it's supposed to draw less than that, based on the voltages across R539~542 which relate to one part of the tone control circuit. According to the schematic, they should be about 2.1V which corresponds to a current of 12.7 mA total, but you measured them at about 3.2V in post #102 which corresponds to about 19.3 mA in that part of the circuit.
The remaining 22.7 mA (to make up the total of 42 mA that the board is drawing) must be being drawn by other parts of the tone control circuit. But trying to figure out exactly where, and why, those currents are flowing is not worthwhile, which is why I suggested replacing the whole lot with two ICs.
I would like to say that the transistors in the tone control circuit have been damaged, or are failing due to age, but both the left and right channels have the same high current flow, and they're independent of each other. So if it's a component failure, it's identical in both channels, which seems unlikely. The alternative is a design problem, but then that heatsink would have been getting hot ever since manufacture, and that would have left signs on the circuit board.
So I'm really not sure what the problem is.
If you like, you can replace all of the transistors on the tone control board and see what happens. While they're out of circuit, you could also measure the resistors, just in case some of them have drifted in value and are causing the high current problem. You can also replace the electrolytic capacitors.
There are four types of transistors on the tone control board:
Q501,503,505,507,511 (left channel) and Q502,504,506,508,512 (right channel) are 2SC2320 and can be replaced by MPSA05:
http://www.digikey.com/product-detail/en/MPSA05G/MPSA05GOS-ND/1482444
Q509,513 (left) and Q510,514 (right) are 2SA999 and can be replaced by MPSA55:
http://www.digikey.com/product-detail/en/MPSA55G/MPSA55GOS-ND/1482498
Q515 (left) and Q516 (right) are 2SB646 and can be replaced with MPSA55 as well
Q517 (left) and Q518 (right) are 2SD666 and can be replaced with MPSA05 as well.
So to summarise, use MPSA05 for Q501~508,511,512,517,518 (12 transistors) and use MPSA55 for Q509,510,513~516 (six transistors). These ALL have different pinouts from the originals.
There are also two diodes on the tone control board - D501 and D502. They are both listed as 1S2473 which is an obsolete type, but they can be replaced by any small signal silicon diode such as the 1N914:
http://www.digikey.com/product-detail/en/1N914/1N914FS-ND/978749
Replacing these semiconductors may or may not reduce the current drain and stop the heatsink from overheating. As I said, take the opportunity while the transistors are removed to measure all of the resistors. If any resistor doesn't measure within ±5% of its marked value, post the circuit reference, the marked value, and the measured value (measure in both directions). In some cases the other components in the circuit may affect the measured value. But with the transistors removed, this will be minimised.
