"250 total direct messages per day, on any and all devices"
http://help.twitter.com/forums/10711/entries/15364
Im not sure if they will make an exception for you. I too wanted to us dm as a means of communicating, but having a limit of 250 in a day would just be crippling.
Perhaps an argument in your d glu would be to allow for "trigger word or phrase" then an open message would not be as bad.
Another option would be you send a tweet with a link. The page has a password which displays the message for the user.
Clearly on the mobile or something, not as important. But bringing them back via the web page. Allows you more options in terms of what to display.
I know you haven't mentioned nor asked. But a potential tier pricing scheme.
1) How many reminders per week / month
2) Maybe allow non paying users the ability to pick 15min blocks, yet allow paying users the freedom to create any.