I have not tried Tylenol PM lately, but years ago I tried it a couple of times and hated it. I woke up feeling groggy and I didn't think it helped me sleep that much better. In retrospect, I should have tried taking it earlier in the evening, maybe an hour or two before bedtime (don't try this if you have to drive during that time) to give it time to begin to work, then, when I went to bed, it might have taken effect more quickly. It would have also given it more time to work through my system so it wasn't still there in the morning.
My two cents on the idea.