I'd agree that it's Alice. It's the normal way that small cs were written (look at vicar, there's also a Michel. ) The reason these records are out of order is that they were never part of a book. They are Bishop's transcripts, a copy of the register that should have been sent just after lady day each year to the diocese.
Some vicars were scrupulous and sent good copies, some sent very poor copies(entries missed, names misscopied) Some vicars didn't send them regularly. There is a big gap following this page until 1662. That's because the system broke down in many areas during the Commonwealth period.
How they were kept in the diocese archives also varied. The loose sheets may not have been assembled in parish and date order until fairly recently.