Could there be a steel nipple on the inlet to the WH?
Have you checked the water pressure in the house? Do you have a checkvalve in the water meter or a prv? If so, do you have an expansion tank? Double-check the T&P valve to ensure it can open. Note, if there's rust particles, it might prevent the thing from resealing again and it'd leak...best to flush until it is clear first before trying that. Excessive pressure cycling might affect the life, but the things are designed for more than should be there if the T&P is working properly.
It would be unusual if the anode rod got used up in that time. Even with a crack, the anode rod should limit corrosion, at least until it is consumed. If interested, google sacrificial anode as to the theory behind their use.