I was reading though Twin Mustang: North American's F-82 At War, and one of the P-82Bs converted to test night fighter equipment did test a small pod with an APS-4 or APS-28 radar unit mounted under the wing. It seemed to be no longer (or even shorter) than the gun pod, and a lot smaller in diameter (it seemed similar to the P-38M's radar pod). I'd be interested in how it would've worked, given that the design of the radar pod was to move the scanner far enough forward so it wouldn't scan the prop blades.
Also in that case, I don't know why a radar pod similar to what the Hellcat and Corsair night fighters used mounted on an outboard wing section wouldn't work.