I participate in many multi-day rides every year and when I was younger, I did stage races. My suggestion would be to have a course that would mirror this.
Ride Scenario: You have a 400-500 mile course (example: RAGBRAI.com or bicycletourcolorado.com). It could be a point to point or a loop. But the idea would be to have a rest station every 20-25 miles, where riders can regroup and take real bio breaks or hydration breaks, and then continue riding. The day would have stopping point at every 50 or 75 miles where the rider can stop and log out.
Race Scenario: would have a same or similar course, but like in a race no stopping at aid stations, it would be fun to see a feeding zone every 30 or so miles. But the racers then would finish each stage be "done’ for that day/stage. The stage race could be like an organized race event like you currently have set up or they could race the stage solo or with whoever is on at the moment.
In both cases, the next time the user logs in, they then can pick up where they stopped at.