I think the sound quality will be horrible through the glass elevator, and leakage out of the shaft might be a concern also. (If it's heard clearly inside the glass elevator, it will be heard clearly outside the glass shaft, right?) I'd look hard for a solution that would use one speaker in the elevator, and some kind of interface with the elevator controller that would fade from one song to another as the elevator moved. The supplier of your elevator equipment may be able to help, I'd think.
Even if you have to have some custom electronics work done, the cost difference may not be that much, as you'll only need one speaker/amp/source, instead of 4 of each, and it won't have to be a big amp either.
I didn't think I'd ever see someone ask what Klipsch speakers to use for Muzak. []