Where can I find recordings of old Chinese pronunciation? Old Chinese phonology and Reconstructions of Old Chinese seem to be two things that keep cropping up every now and again.

Baxter–Sagart seems to be the big one these days.

Are there any recordings of Old Chinese pronunciations available?
I doubt it.  Baxter and Sagart themselves mention, in their recent book on Old Chinese, that the reconstruction is at least partly schematic: The symbols are meant to be phonemic, not phonetic.  Roughly speaking, that means that their main function is to trace the etymology of the spoken language, not to reflect how the sounds were actually realized.  In many cases, they know no more about a particular sound than that it was a consonant of some sort, or sometimes that it was a velar consonant, or a guttural consonant, or some kind of lower vowel, or whatever.  However, they have decided to use a convention that makes sense, that whenever a sound has so-and-so kind of reflex in the modern languages, or in Middle Chinese, then it will be represented with such-and-such a symbol in their Old Chinese transcription.

In reality, in most cases, the sound probably was something like what they transcribe, but not reliably so.  At one point, a few years ago, Baxter and Sagart produced a "simplified" version of their reconstruction, which filtered out some of the uncertainties and made various specific decisions about which sounds went where.  They decided in the end to scrap that version, because they felt it conveyed an unrealistic level of assuredness about the sounds of Old Chinese.

At any rate, even if one were to pick a particular realization of the phonemes of Old Chinese, it would probably take a lot of effort to learn to speak it fluently enough to read, say, Confucius, and no one is going to put in that much effort if there's a good chance a large percentage is just plain wrong.