I find it disconcerting that I can send heads, arms, and limbs flying all akimbo if a target is alive, but once they die they seem to immediately develop some sort of 'iron flesh rigor mortis'.

What if I want to decapitate every person I kill, and collect their heads to build a giant pyramid to the blood god? Why can't I chop them up into little bits?

Sometimes you just want to chop the bodies of your fallen foes into little bits!

Is there a mod that allows this perfectly reasonable behaviour?

To the best of my experience with the game it seems to work just like you want it to work. You might be aiming at wrong place or using a weapon that is not able to cause such harm. Actor models in Fallout have "fixed" location where arm , leg or head would break off. I'd suggest trying a different weapon, like a knife and using grab "Z" button to place the body in more comfortable place to perform such an action.

I'm pretty sure I was able to blow the head off of a corpse...

Corps Limbs are dismemberable

But you can't blow the body to pieces like you can with VATS.

Yes you can, provided you have bloody mess. All dismemberment options are available in or outside of VATS. Trust me, I've done my share of slaughtering in both FO3 and NV.

I've desecrated more than a few Legionnaire corpses by chopping the head off if it didn't fly off already in melee combat. It works on dead foes, just like it did in FO3.

You can destroy corpses after death, I'm not sure if you have to have the "can't think of the name" perk where there is more gore added to their deaths.

No, you don't need Bloody Mess.

True. Hell, I'm using Arwen's Realism Tweaks which even reduces the chance of dismemberment and I've still seen it happen.