Alright, so here is the skinny on how the fix went down.
I replaced the Q15 transistor after discovering that it was the likely source of the fault. Here is the offending part:

After replacing it with another 2n3904 and booting the system back up, it passed the self check with flying colors. The voltage readings at TP7 on the power supply board also read 21.7V, which is within 0.3V of the rated specification of 22V. I checked the frequency output at the top and bottom ranges of the device with my frequency counter (top right of the following images) and everything came out within the error digit of the counter. Spot on!
1050 MHz output @ 0 dBm:

10 kHz output @ 0 dBm:

I did some further testing of the quality of the frequency output with the oscilloscope.
Waveform trace @ 10 kHz, 0 dBm with infinite persistence:

Waveform trace @ 10 MHz, 0 dBm with infinite persistence:

Nice to see that the amplitudes are within a few mV of eachother over the range between 10 kHz and 10 MHz.
Waveform trace @ 100 MHz, 0 dBm with infinite persistence (note lower amplitude due to bandwidth limit of scope at 100 MHz, also the built in frequency counter doesn't seem to work right beyond the bandwidth limit):

Next I did some amplitude testing at 10 MHz output, and everything seemed to check out.
-50 dBm (min output detectable with scope):

-20 dBm:

13 dBm (max output):

Traces all look stable, amplitude looks right at first pass (need to double check).
Finally I tested the AM/FM modulation capabilities at 10 MHz output with the oscilloscope, and again it performed admirably.
FM @ 10 MHz, 0 dBm, 99.9 kHz modulation width, 1 kHz modulation rate:

Simultaneous AM & FM @ 10 MHz, 0 dBm, 99.9 kHz modulation width, 1 kHz modulation rate, 90% AM depth:

That concluded the tests that I have performed on this device. I am fairly satisfied with its functionality. I still have no idea why the UNCAL light is flashing when the output is off, however it goes away when the output is turned on. I performed a latch test (no idea what that really does), but it reads LATchAA as an output after the test. I'm not sure what that means, and the manual hasn't been very helpful yet, but maybe I will learn some more later. Regardless, I am quite happy with the outcome of this repair so far.