I am assuming that the two witnesses who sign the Ketubah are witnessing the actual wedding ceremony. At every wedding that I have attended, including my own, the witnesses signed the Ketubah before the chuppah. If they are testifying that the marriage occurred, how can they sign the ketubah before the event has occurred?
Related to this, what is the purpose of the other two edei kiddushin who are standing under the chuppah testifying that kiddushin occurred? Shouldn't they be the ones to sign the ketubah and do it after the chuppah is over? (AFAIK, there is no halachic requirement that the ketubah be read under the chuppah. This seems to be common minhag.)