ASCAP and BMI use very complicated formulas to divvy up revenues to the holders of the rights. Radio play(both internet and regular), Music purchases (physical and otherwise), TV and Film use and a bunch of other stuff are all complied together and each Rights Owner gets a share. Then it gets divided up in a manner similar to Pirate Treasure, a bigger share to the bigger players and a smaller share to the smaller players. I know a writer who wrote one song for George Strait, his quarterly checks were in the high six figures and a guy who gets a quarterly check of about $90 for two or three albums that did ok (less than 100k units each). That may sound like the formula is totally off but in the big picture it seems about right to me.
Back to the OP, it does seem that your agency is having to pay because you are a “Public” entity but I am wondering if you are paying because you asked for a quote. IANAE in Fair Use but on the surface it would seem to apply in your case.
Do all of your coworkers even *want *to hear your music at lunchtime? Personally I’d rather eat and contemplate the universe in deadly silence (or at least carry on a conversation with my neighbor without having to fight to be heard).
Possibly the “Conventions/meetings…” category would be appropriate, or the “Special Events” category. Filling out the form, and the ASCAP could give you a quote based on the description of the event you give them.
(“Blanket” according to the FAQ seems to involve an annual fee, which would probably be excessive for a one time event).
I got an answer to this question from the ASCAP rep. According to her, in US copyright law, a “workplace” is defined as a public place. It’s as simple as that according to her. I don’t know if I buy it.