I don't really like the idea that the scheduled task should dictate whether its repeatable or even its interval. IMO that's configuration and you should separate Unit-Of-Work from configuration. It makes sense to have some interface the worker-classes implement that exposes something like Name, Description and the actual Execute method. But it should be limited to that. And instead all the interval/repeatable stuff is handled by configuration which can be set through some management in the Console.
And its exactly this management that needs to excel. You should be able to see all configured tasks, their status, right-click on one and choose "Run now" or maybe "Force stop". We can both agree that actually running the tasks is not a big deal. its showing and managing information by the Website Administrator which is tricky. What today is maybe "every friday at 04:00" could easily tomorrow be "every monday and wednesday and friday at 04:00" and that shouldn't require you to change any code.
And its exactly this management that needs to excel. You should be able to see all configured tasks, their status, right-click on one and choose "Run now" or maybe "Force stop". We can both agree that actually running the tasks is not a big deal. its showing and managing information by the Website Administrator which is tricky. What today is maybe "every friday at 04:00" could easily tomorrow be "every monday and wednesday and friday at 04:00" and that shouldn't require you to change any code.