After replacing the drum wheels, drive belt and tensioner, it turned out to be the motor making the noise - a loud hum, not a screeching noise. In replacing the motor I strongly advise buying a new blower wheel, as the old one had pretty much fused to the motor shaft so I had to cut it off. This is also an excellent opportunity to clean out accumulated dust from inside the dryer.
A quick tip here. In the repair video (which is excellent by the way) I found it far easier to simply remove the door switch rather than try and separate the switch coupling. The plastic is very hard to separate without a third hand, and eliminates the possibility of breaking it.