TL;DR-put your actual 1st date available. They're prompt with the info you put

JP Submitted this review about Direct Express Auto Transport
Review made Live: 5/27/2015 8:26:00 PM
Fortunately/Unfortunately, the scheduling company was very prompt to assign me to a company. I wanted to send my car to arrive on a Saturday, so when booking through here I saw something that said "picked up within 7 business days" or something of the like. A week and a half before, my "smart" self thought I'll put that I want my car picked up the Monday before, thinking it might get picked up Thursday to arrive Saturday, since "you know" 3 days in of the 7 business days sounds reasonable for their processing time. Next thing you know I get assigned a company the very next day, saying they are available to pick up my car Tuesday, ready to drop off Thursday (2 days before I actually wanted it to happen). I called the assigned company to try to reschedule, but they always only pick up Tuesday and drive off to all their places for that week (and then it's just a matter of how long it takes to drive to your destination... mine was 2 days...).

So it's service was great and worked well. Don't "try to work the system" cause they system works well and there's no need to do that.