Best I can figure, the 3.5mm TRS headphone plug is being jostled in the TRRS headset jack, which is causing the sleeve of the TRS plug to make intermittent contact with the Mic and Ground contacts in the TRRS jack. With this hypothesis in mind, I ordered a 3.5mm TRRS cable assembly and an inline 3.5mm TRS jack and began experimenting.
My first experiment involved twisting the Mic and Ground wires from the cable assembly together and jostling the plug in the headset jack of the LG V10. This did cause the app to play, pause, and skip forward and backward between tracks depending on how many times I tweaked the plug side-to-side in the jack.
The second experiment was necessary to figure out whether the phone utilized the CTIA or OMTP pinout order for the headset jack. I soldered the Left and Right audio lines from the cable assembly to the TRS jack (both CTIA and OMTP use the tip for Left+ and the first ring for Right+). I then plugged my headphones into the jack and started a song on the phone. While the song was playing, I touched the wire corresponding to the second ring on the TRRS plug to the jack's sleeve (Ground) contact. This caused the audio to play through the headphones, which told me that the phone uses the CTIA pinout order (Tip = Left+, Ring 1 = Right+, Ring 2 = Common Ground, Sleeve = Mic+). If you take up this project, keep in mind that some phones may use the OMTP pinout order, which is the same except that the Mic and Ground contacts are transposed (Left+, Right+, Mic+, Ground).
With the pinout confirmed I soldered the second ring line from the TRRS cable assembly to the sleeve/ground contact of the TRS jack. Because I want to make sure that the second ring and sleeve from the TRRS jack of the phone are never shorted together, I just snipped the TRRS cable's sleeve line off, crimped the strain relief tabs to the cable, wrapped the internals in electrical tape, and screwed the jack shut.
So far, the music hasn't skipped, paused, or started suddenly, and the "Google Voice Search" app no longer starts on its own. In the future, I may use the extra cable assembly and inline jack to build a new adapter that has Vol+, Play/Pause/Next/Prev, and Vol- buttons on a 3' long cable so that I can remotely control the music from a lapel clip while the phone is in my pocket.
Also, it is my understanding that TRS to TRRS cables connect BOTH the second ring and sleeve of the TRRS plug to the sleeve of the TRS jack. This would not solve the problem I have with my phone. If the adapters do, indeed, only connect one of the second ring or sleeve of the TRRS plug to the leeve of the TRS jack, then all I did was reinvent the wheel. That would, however, mean that you have to buy an adapter that corresponds to the pinout order your phone uses (CTIA or OMTP), and I don't see any adapters of this sort listed as having a particular compatability (which is why I am making the assumption that the RS of the TRRS plug are both connected to the S of the TRS jack in these adapters).