How much bigger would a "Thin Man" Plutonium-gun bomb have to be to work?

(Assuming it’s not capital-C Classified)

Some here might already know about the Manhattan Project’s Mk. 2 "Thin Man atomic bomb design—a Plutonium “gun-type” bomb, not unlike the Little Boy bomb dropped on Hiroshima, but much longer.

You’d also know that the weapon design was scrapped when it was discovered that the available Plutonium had impurities that would result in a higher spontaneous fission rate than expected, which would result in a predetonation “fizzle” if used in the bomb as designed—and, as wikipedia puts it, “The distance required to accelerate the plutonium to speeds where predetonation would be less likely would need a gun barrel too long for any existing or planned bomber.”

Okay then, my question—assuming it’s merely “obscure” and not “highly classified”—roughly how much longer would the bomb’s gun barrel have to be to accelerate the Plutonium slug in order to be effective, and/or how much faster than the 3000 ft/s speed quoted in the article?

I’ve not been able to find any credible figures online, on Scribd, or on Google Books. But, I’m gambling on the answer being either unusually boring, or ridiculously huge rather than frighteningly classified. So, there it is: How much taller does the Thin Man have to be?

(And no, for the record, I have no desire or intention of building one of the bloody things. Everyone knows the Plutonium-possessing people who do only hang out on disreputable imageboards, anyway. Duh.)

The spontaneous fission of PU-239 contaminated with PU-240 is over 100 times greater than that of U-235, so the assembly time of the core must be correspondingly fast.
I’m sure the actual dimensions are still classified, but you can get an idea of why the gun-type design was abandoned when the PU-240 contamination of factor-produced Plutonium was discovered.