Thanks, that's a help.
You got loud with the Stereomour control at 9:00 and with the PAT-4 at 12:00. Everything I know says they should have been the same, so I suspect you may have switched the tone and balance potentiometers - that would explain the difference. We can check that further by just measuring the input resistance of the Stereomour with the tone control centered and at each extreme. I think this is worth pursuing, just to be sure the amp is working correctly.
But that will have only a small effect on loudness. Everything I know says that the gain of the PAT-4 with the volume set to the midpoint is 1.0, or 0dB. Which says you don't need more gain. But you do! We can pursue that issue by making real gain measurements on both Reduction and Stereomour. Usually PB recommends using your cellphone as a signal generator, and making voltage measurements at various places including some internal to the amps.
However, it will take a while to get through this exercise. And I completely understand if you need to take a break from this and just get some tunes playing - in which case, you still need some gain, unless you keep the PAT-4 in the circuit. So I'll suggest that you could purchase an inexpensive preamp to get things going - for example, the Schiit Modi [edit - Magni is what I meant] is a $99 headphone amp that works as a preamp as well, and provides 15dB of gain. I have no direct experience with it, but they are well regarded.
We'll keep working on either or both issues as long as you are wish. We're not going anywhere, so if you want to take a break and pick it up again in a couple months, that's fine too.