I've tried your solution -- *without* the pillow! -- each
time it has refused to shut off. So far, it has worked
each time. But, it is very inconvenient -- put the remote
down and forget to check it 15 seconds later (to verify
it has powered down) and you end up with dead batteries!

What brand/model is it? Most remotes -- at least, those with a high-drain
display -- shut themselves off after a user-selected timeout.