OP here. Many thanks for all the responses. I was going to give more detail for what's actually going on, but in fact the question that "hippo" asked led me straight to the obvious solution to this.

As they pointed out, the Catalyst app is already running, and that really is the daemon, and all the workers we need. What's happening now is that we implement our own job queue, and the cron script simply gathers data from the job queue and fires requests into the Catalyst app. Currently, the cron script loads the entire app (because it uses some utility functions that are, um, useful), but it doesn't need to--with a small amount of rewriting, the cron script can get the info it needs, without the zillion database connections, and send everything into the main app.

When I was thinking we needed a separate daemon, I didn't stop to consider why this script itself needed to be daemonized, and in fact, there's nothing in that script that takes much overhead. I was misunderstanding my own app. Wasn't intentionally an XY question, but it seems to have ended up that way.... Thank you!