See, my first action if I was running a free and open source service that used the API free would be to immediately respond and say, "Hey, I had free access because I'm running an open source project that uses this and it provides a free service. Is there no option for me to continue that in some way? If not, I'll have to shut down." Quick, simple, gets to the heart of the matter, and provides the department responsible at Twitter with the information most relevant to possibly letting me continue with free access.

Immediately going public can backfire, depending on the specifics of your case. Now there are possibly competing interests at play, the public pressure to let them continue, and possibly some anger over at Twitter for not being given the smallest benefit of a doubt (when their project works because of the good grace your company exhibited in the first place) or even asked before playing hardball. If I was the person responsible for making the call at Twitter, I would probably acquiesce, but I would want to tell this person to go get bent.