"Which heads should we choose?"
It depends on your intent. If you want to keep the car completely original then you need to find an original J head with an appropriate casting date. Those have become difficult to find and even if you did you will probably need to have it rebuilt.
In my case, I had one of the exhaust port rot through just enough to cause a coolant leak into the exhaust port. Cast iron can be difficult to weld on but it can be done with stainless 308 rods.
We couldn't get the weld area clean enough and the weld keep getting bigger and bigger. In addition, even if we were successful in finally getting the weld sturdy, I would always be weary of it failing in the future.
In my case, I had already gone to a 347 on the original block. I decided to go to AFR 1388 heads shaved down .024 to get 54cc combustion chambers and went to Cometec -027 head gasket.
You could mill off the AFR identification on the ends of the heads, or maybe even get AFR to do that for you, then just paint the heads Ford blue, then who would notice?
These heads will give you better flow numbers then the iron GT40 heads used in '66-67 by the Ford team. In fact they flow better then stock Boss 302 heads do so building a 500hp 347 on a 302 is VERY easy to do.
Of course in a Mangusta how much additional power the chassis will take is just an educated guess. Certainly what I have seen of the few Mangusta race cars still being run, mostly in Europe, they are over 400hp engines, no doubt.
So there are solutions but even just shipping an original set of iron J heads to Japan is a consideration.
I'm glad that the web page helps. It's still surprising to me how many "Ford enthusiasts" have never heard of it or doubt the authenticity of the information posted?