This should do it.
Note that I extended the end plate to 30 seconds and used a Math.min to end the time remapping at 1 frame before 10 seconds, so as to keep the end plate from there on out, which I assumed is the intention.
I suspect the end plate comp needs to be as long as the maximum length of the main comp to allow adequate room for remapping. 13261_promodummycompremapped.aep.zip