The old Hitec 6/10 was state of the art when it first appeared, but used what were probably the most terrible power transistors ever let out into the world. The components that drove them used a lt of power to do so, and tended to heat up to their thermal limit. They had a tendency to grill both themselves and the PCB where they were mounted. It is very possible that over time something has cooked. I would have expected the "forward" circuit to be distressed first.
When the label said "8.4 Volts" maximum, it meant it. When it said 10 Amps current, it really meant it. Back in the day, 540 motors were a sort of standard, that ESC was designed with them and 7.2 volt battery packs in mind. But a lot depends on how the 540 is loaded. A heavily loaded one might want to pull more current than the ESC can supply.
Does the motor show that behaviour when not mechanically connected? i.e. no load. If so, its not the prop shaft misbehaving.
Does it behave like that without the ESC? i.e. direct connection to the battery. If so, its a broken motor.
Does a different motor misbehave when connected to the ESC? If it does, the ESC is the guilty party.
What happens if you operate the "servo reverse" on the transmitter and connect the motor reversed so that forward on the stick is still forward on the motor?