According to my napkin math it would take longer than an hour if the tape was ~3.3*10^218 sec long (or three million trillion trillion… (18 trillions) …trillion years). Assuming you have only have two options to choose between but can pick which alternative in in 5 seconds (2^720) and you want to get down to a 1 minute intervall.
So i mean its not impossible to find a tape long enough though it seems unlikely that we would be so off in our estimates of the age of the universe.
I havent really experienced that tbh. But unlike (seemingly) most people these days I don’t really have issues with falling asleep in general. I fall asleep just fine in hotels. Personally my issue with hotels is that it usually gets quite messy due to the limited space and also I sometimes get a sore back from the too soft beds.