A simple way and what Paragon does is predict the position ahead of the character to determine the stop location, then calculate the distance from your current one to that and look it up in the Curve.
For Start you look at the Distance created between the last standing position and the current Moving Position then you use Sync Markers to have a seamless transition somewhere near the end of the start motion hence why you need a few steps after the actual start motion. Most of this sounds simple but takes a bit of engineering work to get working properly. There have been various samples floating around on how to do this, can’t remember where though.
Seems like Epic is going to publish their solution soon enough :).