I can see that this tennis post is becoming a serious PITA.
Let's try to make the job easier rather than pull harder.
Are you sure you are above the inner rod that is concreted into the ground? Would it get any easier if you used an angle grinder to cleanly sever the outer pole from the bottom surface (I know it's still rusted out inside).
If we must pull harder. The hardware store has a selection of metal rods but a hardened steel bolt would seem like a good choice. You could go to a machinist supply and describe what you want and get a steel rod with more strength.
Another thought is to get more mechanical advantage. Put in a new bolt, thread over it with a square cylinder. Fix the ends with washers/nuts. Use washers on the inside of the cylinder so it doesn't puncture the metal rod. The assembly will be harder to bend when you jack it.
Or if you can find a good triangular brace (like a joist hanger) mount this upside down and jack on it.