Thanks all for your input on this. I'm attaching a clip of the schematic with this opamp in it. To answer questions:
The voltage rails on the opamp are what they should be; +15V on the positive and -15V on the negative. The input+ and input- are both 0V ±0.3 mV, and the output varies from -2.8V to -11.3V when adjusting the main frequency pot (R8 at the top of the schematic). Pin 1 (balance/compensation) is -13.7V (so is pin 5, Balance, but that's not connected to anything). Pin 8, Compensation, is -7.9V. The LM301AN can take a maximum supply voltage of ±18V, so the rails are within limits. I do have to point out that these tests are done on the now-bad chip, and while the first test showed about -.25V on the input-, a second test showed it sitting at 0V.
As far as the replacement part source, it's from a huge cache of brand new chips a friend of mine got at an auction from the electronics maintenance department of a large company, I think a pharmaceutical if I remember right. I'd tend to think they would buy from known good suppliers. It's a National Semiconductor chip, just like the one it replaced, and the date code says 849, which I take to mean sometime in 1984 (please correct me if I'm wrong in that).
It is in fact an LM301AN that I'm using, and which the old chip was. All the system supply voltages check out as perfect, within ±.02V. However, in running through the voltage checks in the calibration section of the manual, I found something that was curiously out of spec in a different part of the circuit. In the trigger zeroing circuit there's a variable resistor for setting zero (I'll attach the schematic). From either side of the resistor R192, it runs to the emitters of the PNP transistors Q42 and Q43. When turning the variable resistor back and forth, the emitter voltage on Q42 goes up and down just as expected, but the emitter voltage on Q43 never moves. It sits right at -1.8V. Coming off the base of Q43 is N2, and N1 after the resistor. N1 runs to another transistor somewhere else on the board which is where I found the faulty voltage point showing -2.5V when it's supposed to be 0V. (N2 runs off to the input+ of an LM301AN opamp in the cap multiplier, which is showing -2.5V on that input+ pin and about -2.3V on the input-.) I don't know if, or how, this voltage discrepancy might affect the LM301 that keeps burning out, but what I can't figure out is why the emitter side of Q43 doesn't budge when adjusting R192.
If this is all clear as mud I can attach the complete schematic with the spots I'm referring to highlighted for clarity.