From my experience of continuation-based web app, what you're dealing with is not a full continuation captured by call/cc, but rather a delimited (partial) continuation, which captures the continuation of your application logic but not the state of underlying protocols. You can implement delimited continuations on top of call/cc, and I did based on Gasbichler&Sperber paper (ICFP02), but in most cases explicit CPS wrapped in some macros are just as well worked.
