I see the answer depends on 3 main things:
1. Car consumption - how much wattage per mile the car needs (accounting for weather, terrain, battery size, speed, congestion)
2. Time to get off intended path to get to and hook up to the charger
3. Which battery charge rate (60kWh, 85kWh Atype, 85kWh Btype)
based on my estimations of the above
95-110 miles for an 85kWh B type battery car using .35 - .4 kWh/mile and taking 7.5 minutes to go off course and hook up
65-90 miles for an 60kWh battery with same usage/time
85-B would charge 18 minutes and 60kWh would need to charge for 30 minutes each stop for ideal travel time.
Other minor assumptions that would be needed to take into account.
4. Range anxiety (buffer needed) ( best case is 5-60% state of charge)
5. Time needed for other things people do during stops (getting food/eating/shopping/other stuff...) - this will be variable based on starting point and what is close to SC. (may take over 30 minutes to go somewhere and get back)
6. ratio of 60kWh cars vs 85A-type vs 85B type
looking at time it takes for charging to travel 500 miles:
The 85kWh+ battery size looks even more desirable for long distance driving.
So based on this - I see distances of ~95 miles between chargers as ideal.
[edit - added 85kWh Type A curve]