Scheduled event won’t fire

I’m trying to set up individual, one-time schedule events in a plugin. No matter what I do, I can’t seem to get the events to fire. I’m using the Cron View plugin to see what’s in queue, and the events are added and remove themselves totally on schedule. I never, however, receive the email I’ve set to send in the action’s target function (simply in order to test the event, there will be more in there later). I have tested the function outside of scheduled events, it does work. Here’s some code:

GLOBAL $new_workshop_id;
$new_workshop_id = $wpdb->insert_id;

function send_reminders() {
 GLOBAL $new_workshop_id;
 wp_mail('my@emailaddress.tld', 'Automatic ID: '.$new_workshop_id, 'here it is!');
}

if (!wp_next_scheduled('send_reminder_emails_'.$new_workshop_id)) {
 wp_schedule_single_event( time()+30, 'send_reminder_emails_'.$new_workshop_id );
}

do_action( 'send_reminder_emails_'.$new_workshop_id );
add_action( 'send_reminder_emails_'.$new_workshop_id, 'send_reminders' );

One thing I’m suspicious is the placement of do_acton and the function itself, send_reminders(). The above code is within some if statements checking for POST vars, so it’s possible that the function can’t be accessed by the CRON job – so where should I put the function? I’ve tried right at the top of the plugin file. From what I’ve read, do_action should call the function and execute it wherever you have put do_action, but I guess I need to know where to put send_reminders() in the first place so that it’s accessible, by either the cron job or do_action.

Thanks in advance for any input!