The rotational rate of the earth slows down by about 0.002 seconds per day per century, due to tidally induced transfer from earth's rotational angular momentum to the moon's orbit. The rate of energy transfer is about one gigawatt.
The amount of energy (and mass) required to "eliminate the tilt" is staggering. It is probably not possible to do at any cost. (We might as well eliminate the eccentricity of the earth's orbit while we're at it.)
The effects of eliminating seasons would be disasterous, short term. Maybe he should have concentrated on something more practical, like maritime safety.
you're right, Tesla tried to get him to fund Wardenclyffe. (I'm not even sure whether I'm being sarcastic or not)