Thanks James, that's exactly what I needed. I was looking for polymer caps on DigiKey but wasn't sure I'd found them; with that part number I was able to find where they were hidden, and actually I see now that "polymer" is an option in their parametric search for tantalum caps.
Well ten bucks is a lot for an SMD cap but the shield cost more than a hundred to begin with, and my truck cost many thousands (that's where this is going), so I'd be losing a lot more that ten bucks if a fire broke out.
Pardon my noob-ness, I don't know much about different capacitor types, just generally what a capacitor does. Is there any reason, other than form factor, that we couldn't use an aluminum electrolytic for this purpose? Certainly you can get very high capacitances at high voltage ratings for very cheap, but maybe there is something about that type that is unsuitable to this purpose.
However we use electrolytics as backups in RC planes for exactly the same sort of situation - current spikes on the main power source (battery) that would cause the receiver to brown out, if not for the capacitor to power the device. This sounds very similar to the description given on the Arduino GSM page for why the orange cap is on the board.