Suggestions needed: Best way to take appointments from non-website members?

New to these forums, fairly new to wordpress, but I’m in need of a place to bounce ideas and ask for suggestions! I do this with a few different tech communities, and they have proved invaluable…hope this is the place for that kind of WordPress help!

Currently I’m looking for suggestions on the best way to take appointments; but in a sort of unique way.

I have a friend/client who’s dream is to rid the world of human trafficking via prayer and action: i.e. a person commits to pray for 30 minutes and donate $30 to the organization of their choice.

The cool part is, she wants every half-hour slot, every day, for a year, filled (that’s roughly 17,520 half-hour slots)…so she needs a way for people to sign up for the timeslot they want (first see if it’s filled), and tell what organization they are going to donate $30 to.

(We’re assuming most of these slots will be filled by “unique” volunteers, though we also imagine lots of folks will want to sign up for more than just one time slot.)

Some necessities are: reminders, approval of the timeslot request (and the slot marked as “pending” until approved).

I’ve tried the following plugins, but none of them do what I want, and/or aren’t customizable:

Wp-simple-booking-calendar
Booking Calendar
Events Manager
Event Espresso
Appointy Appointment Scheduler
CP Appointment Calendar
Appointzilla Appointment Calendar

So…suggestions? I don’t mind a paid solution as long as it’ll do what we need it to do, but I’m no programmer (just barely know enough css to create a simple child theme), so it has to be something I don’t have to edit (much).

Thanks; hope this is the right forum to ask this question in!