I have thought about that, but as the app is client-run only, the most direct way I could do it would be to provide a WebService (that is, a process that Chrome or Firefox keeps in memory that can wake up and do things on a timer). This would require that 1) you load the radio via https, 2) your server is https and not on a self-signed cert. Chrome has very particular requirements regarding web services.
Those requirements rule out quite a lot of systems (including my own at present).
I do have an idea that could at least fire the regen-all by a single url. E.g., go to
http://subfireplayer.net/radio/#regenAll and it would automatically fire off the regen-all process (and then strip out #regenAll so it wouldn't do it again). It would mean first you'd have to log in on that client first, so I don't know of Tasker can manage that. Also, the memory load from caching (temporarily) all of the folders, artists, and albums fetched can sometimes be bigger than Android browsers can handle.
But on the desktop, combine that url with an extension that would open a tab (Tab Schedule from Chrome looks promising - nevermind. doesn't want to work at all (oh, one called Crontabs seems to work, and it'll auto-close, too)) and maybe things will work.
I'll give that a try in the next week or so. I wouldn't mind a fresh cache every morning either esp just to get unique playlist/station artwork every day.