The book Mission of Gravity describes a planet with a mass of 16 times Jupiter spinning at a rate of one revolution every 17.75 minutes. This causes it to stretch out into an oblate spheroid and has an effective gravity of ~3g at the equator but a gravity at the poles that varies depending on how you calculate it from either 275g right the way through to 700g.
Leaving aside the improbability of the planet forming without gathering enough hydrogen to become a star, and without losing that enormous spin, and managing to cool down enough...
What I don't understand is the surface configuration. The force of rotation will indeed counteract gravitational pull so you get an effective 3g gravitational pull at the equator. However that will also cause the mass to move towards the equator, reducing the gravity at the poles.
Modelling this planet at my head then anywhere that effective gravity increases in strength is effectively lower potential energy "down" from anywhere that it doesn't. I would expect this to cause the planet to deform and reshape so that the effective gravitation was equal at all points on the surface.
In other words it would be 3g everywhere, because at the poles it would be much thinner than at the equator, but not have the spin throwing you away.
Is this mental model correct? Or have I missed something? Is the fact that the spin is throwing you away from the poles the missing factor?