I should add that one of my plans with the alarm clock app I've been (slowly) developing is to add a setting to allow an on-screen clock which sits in a user-defined area of the screen all the time, regardless of info mode setting, what mode the player is in, etc. This is something I've always wanted because I think it's silly to combine timecode of a song and the time of day into one setting, and foolish to think that the clock visual is a good enough solution for a device that's got so much flexibility. Why should info modes, your choice of visual, and on-screen clock display be mutually exclusive in most cases?
The problem for me now is that Hijack does not currently let applications display a window on the screen and then return control back to the player (kinda like running an Xterm window in the background). Technically the user apps can let all the button presses pass through, but you can't access the hijack menu until you "quit out" of the app, which means the hijack menu would be disabled while this clock overlay was displayed, among other limitations.
So until the user app interface changes a little, I can't really implement a usable on-screen clock. But given this feature, it'd be easy enough for me to do. Once Mark digs back into Hijack a little more I hope this interface is looked at more closely. However I don't think this would be one of the easier things to implement, so it might take some time.
This doesn't really do anything for your "clock while Empeg is off" request, but I think it's an interesting aside.