Well there is a way to get the song details, but it isn't very user friendly.
For example, I just tuned to the 3820H transponder.
Looking at the TSREADER display, I opened up the Program 25 PMT at the left, clicking on the "+". You see then the audio stream at PID 275, and another ES at PID 290. That 290 PID is the stream that has the song info.
If you go up to the "Record" tab, and select "Record PIDs", select that PID 290, and give it a filename with a .txt extension (even though most of the info in the stream is binary), and let the record run for a few seconds, then click the record PIDs again to stop the recording. You'll then find the file you just recorded, and double click on it to bring it up in Notepad. Notepad will ignore the non-text data, and print the text data. I just did this as an experiment, and got:
Not pretty, but you can see the info.
I really wish that TSREADER would output this info directly by just clicking on that stream at the left, but it doesn't. I'm sure that it's possible to create a plugin for TSREADER that would print out the info from these info streams, but I don't know anything about creating plugins for TSREADER, although it is something I'm really thinking about learning to do, because I too would like to see song info from these channels.
BTW, the channel info in the G14 music mux show up in a video stream for each channel, but that is unusual for these music transponders.