Towed tandem nuclear-electric aircraft

One of the biggest problems with your species' crude nuclear fission reactors is radiation shielding.

Fortunately there's a useful bit of Physics called Inverse-square law.

So, to build a viable manned (i.e. passenger carrying) nuclear aircraft, proceed as follows:

Put a closed-cycle fission reactor and electrical generator in a robust airframe with some token shielding.

Take a conventional passenger aircraft such as an A380, replace the gas turbines with electric motors, and stuff the now redundant fuel tanks with Li-ion batteries.

Connect the tail of the passenger aircraft to the nose of the reactor aircraft with a long towing line from which an electrical cable is slung.

On takeoff, the front aircraft drags the rear one into the air using battery power. As soon as a safe* altitude is reached, the reactor is diverged, powering the towing aircraft, plus its own engines, and recharging the batteries. Simple distance and inverse-square law protect the humans from the radiation.

The combination has, for all practical purposes, unlimited range.

Should the cable part, the passenger portion has enough battery power to make an attempt at a controlled landing, although a go-around might not be an option.

* for a given value of "safe". Check regulations in your locality before withdrawing control rods.