I figured it was unlikey that two motors failed in exactly the same way.
Why, was it two different persons ruining them in two very different scenarios?
You can be pretty sure that the H-bridge in a servo has a voltage drop and perhaps there's a sense resistor dropping some too and a digital servo runs at a higher update frequency internally, so it's a safe bet that the motor doesn't see 5V - try a lower voltage, the motor is most likely OK.
Was it perhaps coreless servos?
While it's close to being a crime smoking a coreless, it would explain the high current.
Well, lower the voltage!
Perhaps start from around half a volt and work your way up to the 400mA or whatever it can take without getting too hot.