Does each polyline measure start from zero (their from-end) and end at some length ( the length of the polyline, thus its to-end).
If so you can create point events along each polyline with the route ID being the unique polyline ID (FID) field. The event distance would be the length of the line - 1 foot. So create a non-spatial table with a route ID field which would be the FID value and another field which would be the measure field.
Hopefully your polylines are longer than 1 foot...