The stethoscope would work but then you need (should) to set the hoist up so that the wheels aren't hanging all the down when your spinning it up. You could get yourself "chassis ears" much more better and safer, a bit of money out of your pocket but good excuse to buy another tool!
The bearing could go for a looong time before it's bad enough that you can tell for sure what/where it is without doing something to pin it down.