My god, this was so much easier than I had thought. After a good friend of mine hooked me up with a pre-patched file, it was a simple task of extracting the file and burning both ISOs to two CDs. I popped the first disc into my modded PSone (for imports; I don't pirate), and it booted just fine. I can now play Policenauts in English.
The voice overs are still in Japanese, but who cares when you have beautiful English subtitles? I can't comment yet on the overall quality of the translation, as I've been busy with other games and haven't sat down with it completely, but this week that will change. I've been staring at my Japanese copy of the game for years, and now I can finally enjoy it!
Those who don't have a modded console can play the game just fine via emulator, and while it's not on actual hardware, it's better than never being able to enjoy Policenauts at all. You can find the patch at The Policenauts Translation Project, so grab it and enjoy all the hard work these good folks put into this translation.