Okay, then there must be a fair amount of transformer gain on the output.
The very first thing to do is check the power supply. Make sure it is near 24V. If not, fix that problem, then move on.
If I am guessing right, you are on step 49 of the procedure, Fine Bias Adjustment. The desire here is to set the DC operating point at the middle of the power supply voltage. The power is regulated to 24V, so midrange is 12V.
The way they suggest doing this is to "gently" overdrive the input and adjust the bias so that the output exhibits the same level of clipping at the top and bottom of the waveform.; that will be near 12V, but not exactly. The instructions say to set the gain switch full CCW then go 5 clicks CW. Looking at the front panel photos, I read full CCW as 15dB and five clicks CW from there would be 40dB for a gain of 100. That means a 0.5Vpp waveform on the input should be 50Vpp on the output, well outside the power supply range. All this means is there is a fair amount of transformer gain on the output, maybe 10dB or more.
The output driver is a 2N3055 (that should be the one in the TO3 metal case on the heatsink) and another indicator there is some significant gain in the output tranny. The collector is the case on these, so real easy to get to). Measure the DC voltage (with no input drive) from collector of the 2N3055 (the metal case of the transistor) to ground. it should be near 12V, say +/- 2V. If significantly off, adjust the bias (R39) to get it near 12V. If you can't do that, check the values of R38, R39, and R40. On R39 check the resistance between both outer legs and from the tap to each leg. Trimpots are notorious for the wiper being open.
If everything is OK to this point, give R19 a twist with a screwdriver while applying your 0.5V sine wave. This is a gain trim. If it has no effect on the output, make sure R20 is in place and if it is, it really is 0 ohms. If everything is OK there, check R19 like you did R39 and make sure the resistance at the tap really changes when you turn the scres, then go back and double-triple check the resistors on the gain switch. Since you can back off the input signal and things look good I doubt there is a problem in the preamp (Q1, Q2, and Q3). It is either in the gain switch or the output driver. If you can rule out the driver, be very suspicious of the gain switch.
To test the gain switch, I would crank back the input to a distortion free level, then run the gain switch through each setting. You should see 5dB steps (about 1.8X) gain change with each click comparing output to input on your scope. If you don't see that, then it's either the switch or one or more of the associated resistors. I have, over the years, encountered many open resistors and mismarked resistors direct from the supplier. Now, with the uncertain origin of so many parts that sort of thing has gotten worse. I always ohm out resistors now; partly because my eyes are bad and partly because it's a lot easier to find a bad part before its installed than after. The days of factory tested resistors went away in the early 80s. Also, as a last ditch effort, ohm out the switch.
One last thing - I have looked at 7th Circle designs over the years and consider them one of the best modern designers around these days. They pay attention to things most people don't even think about, life RFI/EMI. Most of the stuff I see these days I wouldn't trust within a mile of a dimmer bank. This stuff I would take to any stage in the country. But the output tranny has DC on it. All I know about it is it's Carnhill. Trannys need to be designed for DC or they become magnetized. Ian can probably tell you more about why that's bad; all I know is it's bad. These guys are smart enough to spec the right tranny, but that is one thing I would want to be certain of before I plunk down $$$ on a preamp.
I got long winded but sometimes it takes a lot of words to explain something. My troubleshooting approach has evolved over the years and may not match yours; that's ok so long as someone figures out the problem. In this case, all prior comments point to too much gain, which suggests an issue in the gain switch since everything works with lower signal. Why not start there? Because life has taught me to check the basics: power first, always. Then, check the DC operating point. Then, if that is ok, do what your brain told you to do in the first place. YMMV.