Simple scheduling/booking plugin needed

I know there are a lot of these, I’ve spent the last week trying over a dozen out, but I think I must be missing something…

Here is the situation. There are two sites that need to be visited by a consultant daily. There are about 24 consultants, and they schedule to travel out to one or both sites if it is convenient on any particular day. I would like to have a page that allows a consultant to easily put their name down for either or both of the sites, and for others to see who has scheduled which days, and which days still need a consultant.

So here is what I need;
– a calendar for each site showing at least the next two weeks
– calendar shows who has already scheduled, and which days are free
– book a day by clicking on the calendar
– calendar visible to logged in members only

Bonus features
– gets name and email from log in
– email confirmation and reminders
– free, and no signup for an external account

Despite spending a lot of time trialling various plugins I haven’t had any luck, and I suspect there might be another category I’m missing in my searches.

Thanks for your help!

Ian.