Would it be possible to determine if your phone was connected to a Stingray instead of a regular cell phone tower? Could you have multiple phones spread out geographically and attempt to triangulate the "cell phone tower" itself, to see if its moving?
Sure, you could probably see if your cell tower signal is moving, and triangulate it. Probably with just a regular SDR-RTL. Ever better, if you can control your phones signal strength, you could ghost your location by boosting and reducing your signal if and when you detect the tower moving. Bonus points if you can fool the stringray that you are traveling at impossible speeds, like for example the speed of light, around town, ... going through mountains, under water bodies, underground, etc.
GSM relies on some extremely precise timing information that both your phone and the network need to be aware of. You're going to have to do more than fake the signal _strength_.
Assuming it looks the same as a normal tower, you could still make a map of existing cell phone towers (crowdsourced from the phones themselves, or there's probably a regulatory filing somewhere with the information). If your connection is better than it "should" be, you may have found a Stingray.
I don't think you would even need to use the signal strength. You could just flag / block cell towers which are newly detected (say 24-48 hours). Crowd sourcing seems pretty perfect for this, and it's not like new cell phone towers are erected that frequently.
It looks like this website may have that information http://www.cellreception.com/
Establishing a baseline signal strength might be difficult due to environmental factors.