I would tell the client the spec changes mean the project will take longer and cost more. (BTW, the schedule as enshrined in the contract terms only means what you and the client say it means.) Be prepared to either tell them how much more money so they can add to escrow, or propose (insist on) an hourly contract because the in-progress website means you don't have an established style to work with. If the latter, be sure they understand to close the original contract for the right reason, so you don't get unfairly penalized for a "bad" outcome. Ordinarily, it's best not to bring up feedback with clients. But this is an exception.