I mean, as far as I am aware, that problem is due to the propulsion method. Would a nuclear based rocket not be able to solve this issue? My understanding is that it would.
Perhaps, but my intuition is it wouldn't make a whole lot of difference, because the reason you can't get off a heavy planet is because of an exponential runaway effect.
An experimental nuclear rocket from the 70s nearly doubled our "payment energy". It should greatly reduce the initial and total mass portions of the rocket equation as well. I don't have all of the numbers to punch into the rocket equation to figure out things exactly, but the exhaust velocity and initial/total mass make up significant portions of the equation, and increasing the former while decreasing the latter will make significant impact on the ability to leave a more massive planet.