Scheduler incorrectly uses initial unscheduled-ness and timestamp for inputs with ROI

#6822 added detection of inputs that start out unscheduled, yet it fails to consider regions of interest (ROI): if an input skips over its start point, it should not actually start unscheduled.

Similarly, the scheduler uses the very first timestamp in the input file to determine the initial time-dependent assignments of inputs to outputs: yet inputs that have ROI should use the timestamps at the ROI start point, not the very first timestamp.