Thanks, everyone, for the input.

I realized the problem when comparing a reference/evaluation board for the modem (which works) and my client's board. It turns out the evaluation board has the entire footprint of the modem with exposed copper going to ground. Our board didn't expose copper below the modem even though there was a ground plane immediately under the soldermask in that area. So I scratched off most of the soldermask in the modem footprint on our board so that the metal casing of the modem (which is already connected internally in the modem to ground) would also touch our ground plane over the entire area (several square centimeters) of the modem.

That did it. No more noise on our power supply. Needless to say we didn't find any mention of this apparent "requirement" in any manual or datasheet that we were given or able to find on our own.

Thanks again!

Regards,
Craig Steiner