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If the starter is cranking slow, it is usually a sign of insufficient current to the starter, either due a weak battery or a poor electrical connection.
Either of these problems can cause a starter to "run on", due to the configuration of the solenoid on these old systems.
Don't know if the OP fixed the problem but Dan is correct, a starter can stay engaged due to low supply voltage, most likely a bad ground by reading the issue plus getting hot. A bad relay won't have any effect on the slow cranking issue mentioned, it only knows engage or disengage.