Sounds like a local LLM, coupled with a periodic wake up signal, will be your pony. Presumably even a small one could run a schedule under those (very reasonable) constraints. Maybe not general pathological cases, but ordinary cases. You'd probably want things to run in one big prompt over time and the tricky part would be finding the minimum size required to properly execute the schedule. Too small, and it loses knowledge of the past. Too large, and it won't function at all.
EDIT: I believe in sysadmin llms and think they will become common and obvious in the next few years. I will look back at the downvotes on this comment with great pride. So, thanks and keep them coming!
I am serious. It may seem like killing a fly with a sledge-hammer, but a local llm sysadmin process has a lot of application apart from cron. The ability to simply talk about your processes in natural language is a huge bonus to those who don't do sysadmin daily - which is most of us. Obviously, using an llm is not appropriate where size and precision are required. In that case use cron and accept its limitations.
EDIT: I believe in sysadmin llms and think they will become common and obvious in the next few years. I will look back at the downvotes on this comment with great pride. So, thanks and keep them coming!