> However, that "non-skip" thing was always a showstopper. Undiscovered music is often obscure for a reason, and I would end up exhausting my skips fairly quickly.

I have a bunch of different Pandora channels with different themes.

Pandora's skip limit is per-channel. If you run out of skips on one channel, and give up on it and start playing another channel, you get the full complement of skips back. You can go for quite a while if you have several channels.

In a development that is probably not related, but nevertheless feels like it is, Pandora tries hard to get you to collapse your channels, playing songs on one of them that don't fit at all but that you've thumbed up on another channel.

(Another obvious pattern is that if you haven't signed in to Pandora in a while, all of your channels will heavily feature songs that you've already thumbed up. They start playing new potential "discoveries" only after working through a "welcome back" backlog.)