I assume this has been asked before, but… if I have a client hooked up to a TLS server with multi-day intervals and I want to trigger it to re-run all queries in the pack 'scoped' to the client, there's no way to restart the interval counter via HUP'ing daemons or something client-side, is there?

I don't think there's a client side way. From the the server you can change the epoch. We've talked about some kind of acceleration for scheduled queries on boot, but it's just talk