Actually, we made TWO of the Exact model 502 generators. The first was around 1970. The second, which you have, was after Jerry Foster sold Exact to Dynatech. They were then relocated from Tillamook, Oregon to Nevada, and went out of business a short time later.
All analog Exact generators had the same basic circuitry; opposing current sources would charge and then discharge a timing capacitor. This would generate the triangle waveforem. The comparator with hysteresis would also create the square wave. The triangle wave was fed through an op-amp with three (four in our high end generators) diode bridges that would produce sine distortion as low as 0.3% at the lower frequencies.
I'm not sure changing op-amps is going to gain you anything. From what I recall, most of the 741 op-amps were used in the current source circuitry, and not in the output stage, which was discrete. The 502 that you have came a little after my time, but the circuitry looks to be the same idea.
I doubt I have a manual for yours, but feel free to e-mail me directly at mkepp@hevanet.com if you have any questions.
Mark Keppinger
Exact Electronics, 1975 - 1978