I suspected the internal preamp was the most likely culprit, so I followed this tutorial describing how to bypass the preamp entirely and push the untouched phono signal straight out to the RCA cables (which I may replace with jacks soon, instead). Honestly, there's not much too it. You just cut out the board and splice up the RCA cables directly to the red/white/ground wires.
|The removed preamp board.|
I was pleasantly surprised when, in addition to fixing my channel dropout problem, the sound quality seems considerably better in the high frequency range. This improvement is why most people do the mod in the first place, and the above link contains some pre-mod and post-mod recordings to help potential modders decide if the improvement is worth their time and effort. I could not distinguish between the two recordings in ABX testing, but the difference in person is easily noticeable. For example, the natural crackles and pops on the records were very subtle and difficult to hear pre-mod but are easily audible post-mod. This may not sound like a particularly positive development, but it's unsettling to think that I was losing that much sound off the top before.
*I was able to piece everything back together with some super glue, but you can also purchase them new from Audio Technica (you can email their customer service) for around $30.