@Robert, your application is not really what PlayIt Live is aimed at but I think you could do it with a schedule as you suggest.
Putting the jingles in a group and setting the rotation rules might let you do something like you want.
There are potential levels and loudness issues with doing this, either the stream or the jingles might be louder although since you can control the level of the inserts you may be able to achieve an acceptable result.
I do appreciate it's a sledgehammer of an application to crack a nut.
Yes, already finding the levels an issue in my trials.