Unfortunately, after many improvements, once the stream finally started working properly—meaning I could stream video for several days in a row without a crash or being forced to manually restart it—the TV itself started fading and flickering. It looks like this TV simply wasn’t built to run 24/7, and it was already old to begin with.
The good news is that my setup works with any monitor. So someday, if I find something else to stream to, I can just attach this already-configured Raspberry Pi.
Also, the Raspberry Pi setup itself is in good shape at this point, so I could make a backup of the whole system.