You appear to have gone through all the steps to confirm a bacteria / anode interaction. I think you are right to go with the power anode. It should protect the new heater from a tank rusting problem and should eliminate the smell.
I too would leave the heater installed and cut the anode as you remove it. Needless to say, use a vise grips clamped on the lower section as you saw through the anode to keep the lower portion from dropping back into the tank.
Once you get the anode out. Chase the tanks threads with a small brass brush or even better, a 3/4 – 14 NPT tap. Then pour in 2 pints of 3% hydrogen peroxide. Then install the power anode following Randy’s instructions and enjoy the results.
Post your experience and the results for all of us to learn.