You can't get there from here with real physics.
The amount of oblateness is related to the amount of spin. If the centrifugal force is anywhere near the gravitational pull, then the atmosphere will all drain off of the edges.
This answer provides good calculations on how oblate your planet can get before it rips itself in half. Spoiler: it's roughly a 3:1 ratio.
On the rotation/orbit thing, I don't believe that you can have a 24 hour orbit at a distance that also corresponds to the goldilocks zone for habitable life. I'd have to do a bit of research to figure out if a planet could precess that fast without ripping itself apart(retracted, but I think that would significantly reduce the speed of spin.please see below)
On the rotation/orbit thing, I don't believe that you can have a 24 hour orbit at a distance that also corresponds to the goldilocks zone for habitable life. I'd have to do a bit of research to figure out if a planet could precess that fast without ripping itself apart, but I think that would significantly reduce the speed of spin.
So, sorry, in an environment where Niven couldn't get away with God's Easteregg, you couldn't get away with this. Maybe you can crank your suspension of disbelief up a couple notches.
Addendum: After a little research, I found the possibility of an actual moon-sized object orbiting a white dwarf roughly every 24 hours, within the habitable zone of that star. As such, your crazy-fast orbit is actually MORE likely than the pancake shaped planet.