... I measured the temperature of the heatsink to be 250F or ... 300F or so after having played at full volume. ... At max volume and aggressive playing, the dissipation would be ~2.5W with the 5881 tubes and ~3W with the 6L6GC tubes. I assume this should be within a comfortable margin of the 5W diode rating. I looked up the specs for the zener diodes I bought, and they do say max operating temp of 200C which is close to 400F. ...
I haven't used zeners for voltage adjustment, so I can't tell you how hot is "normal". But just like with resistors, the closer the actual dissipated power in the zener gets to the rating of the device, the hotter it gets. If you were using 10w zeners, they would run cooler. If you used even higher-wattage zeners, they would get cooler still...
The currents you were measuring sound about right for peak current draw at max output for a ~50w amp.
Why not use resistors?
Ohm's Law is why.
Volts = Current * Resistance. If we used a resistor to drop voltage, then there is little voltage drop when current is small (idle) but very big voltage drop when current is big (full roar). So the voltage drop is non-constant.
A zener used within its ratings gives a constant voltage drop. So the lowered supply voltage is consistent at idle and at full roar.
... Assuming you want a 50V drop then you're at 480V. So 50=(0.075)R gives 667 Ohm's. A 670 ohm 4W resistor on your B+ should work.
75mA * 50v = 3.75w. A 4 watt resistor will get screaming hot, though it shouldn't burn up. The common rule of thumb is use a resistor double-wattage the expected dissipation, so 7.5w and probably rounded up to a standard 10w part.
That's fine for idle, but osing pointed out the current is as much as 300mA at full-tilt. 300mA
2 * 670Ω = 60.3 watts. Your 4w resistor (or even my 10w resistor for the idle current) just went "poof"... And before it did, it tried to drop 300mA * 670Ω = 201v instead of the original 50v.
Also why on the CT? ...
The idea is consistent reduction of voltage, right at the power transformer where the original a.c. voltage is provided to generate the B+ voltage. And the reduction is created by shifting the PT winding's relationship to the reference point of "ground".
The PT's voltage is from the end of the winding to ground at the center-tap for a center-tapped high voltage winding. The zeners move the center-tap 50v "below ground" so the CT appears to be at -50v relative to ground. But the voltage of the winding from CT to the end of the winding hasn't changed. When you measure voltage from end of the winding to ground, it appears to be the winding voltage minus 50v.
Hypothetical example:
You have a PT with a high voltage winding of 340-0-340v. With a solid state rectifier, you'd get 340v * 1.414 = ~481vdc (minus diode drop). The winding looks like
340v (winding output to rectifier, filter cap)
0v (grounded CT)
You add a zener string which moves the CT 50v "below ground". The winding now looks like
290v (winding output to rectifier, filter cap)
0v (grounded filter cap at rectifier output)
50v (voltage drop across zener string, with CT on non-grounded side)
Total winding voltage is still the same 340v it was before. But the filter cap sees a rectified 290vac, for a rectified 290v * 1.414 = 410vdc (minus diode drop).
And with the zeners, the rest of the amp sag/interaction at high volume is unchanged over what you'd have if you just wired it normally but used an actual 290-0-290v PT.