Here are my proposed solutions:
Problem 1) Design a road that is always flat on certain days.
This is currently only possible via the API or meticulous use of the take a break option, and beeminder will ruin your road if you derail or retroratchet or change you road dial. Fixing all these Beeminder issues would be a great help.
(I guess this is the same as the solution 1. you listed but I think it is the Right Thing to do, so keep bugging @dreev about the Road Editor and fixing Beeminder to not do horrible things to your custom road.)
Problem 2) Use use GTBee to set up a task to clear eep X by Y o’clock.
I think this is equivalent to your pre-committed data points idea but doesn’t involve changing Beeminder’s day sized resolution. (See also: Continuous beeminding)