Well, I'm going to call a mini-victory here in that I think finally we're asking the right class of questions. Not that we have the answers yet, or that the discussion is over, not hardly, but we never would if we didn't have a clue what to be looking for. I started down this path due to some rather interesting hints handed me on a silver platter by nature, but this is where they lead, and once here, it seems we can flesh out some reasonable explanations that don't require magic or new science even -- just new technology. Should be a snap, right?
Of course, the hope is we get to a place where this suggests a do-able experimental program, and I think we're getting there. Sometimes the universe is its own best model and it does run in real time by definition. So we think of some things to try, measure what they produce based on these ideas, and see if we're onto anything with them. And expect some surprises that might illuminate our understanding further.
I can imagine a way to get D's to hit P's-first if we are thinking pure - classical mechanics. If they're spinning (near certain) quickly (the numbers would seem to say so) then having the right spin about the right PN axis might make the coulomb forces only change the spin phase as they approach, so by getting the phase right way back there could end up with them hitting PP. It'd be darned tricky/subtle to do at the spin rates and transit times involved (lots of turns on the way in) but at least kinda possible in imagination. If you knew how you wanted them to hit, I believe you could get it done, no matter the two orientations and angular momentums you wanted, almost. There's that quantization of angular momentum (and various other things), and maybe the reason that good reaction is so rare is that no easy combo of two D's adds up to a legal eigenvalue for an He? I'd have to do more homework on that one. If there was a mismatch, perhaps something like a nearby photon could act the same way a catalyst does in chemistry to help two reactants get aligned right for easy reaction...or something. (really getting out on a limb here, as you'll know) If I knew all the allowable quantum numbers for an He, and for the sum of any two D's, then I'd know something, so I guess I gotta go learn what those all are. If you have to break some conservation law to do it, that'd explain a lot about why it's not common -- and maybe how to do it, perhaps with some intermediary to make all the laws happy.
Now if you go sub-nucleonic and start thinking about quarks and gluons, and the fact that a proton is only net +1 (but really composed of other sub charges that add to that) and a neutron net 0 charge, yeah, then it gets a lot fancier to imagine, but maybe not harder to actually do, as those kinds of forces have real short range, so you'd still be in a mode of getting the classical stuff set up so that would take over once things got in range.
Has anyone mentioned (eg the big science boys) that perhaps some of the stuff that binds the P and N's might be quark exchange, and not just gluons&muons? How would you know, if presumably one up quark of some color is just like another and color exchange is common? Where/how does the identity smear out in such a case? That opens another huge kettle of fish, not necessarily making it harder, other than to model/understand. But you're right to mention it as something that would have an affect in this. Or to paraphrase your "call a hadron in vacuum" line -- is it really two discrete particles in a D, or just a big blob of quarks that only look like two particles after you split them apart and all the sub particles have to choose? I'd guess we're right at the line where it could be "some of each" in the quantum-fuzzy world. But as you pointed out, since they have a polarity (or a moment, whatever), then we can still tug on them with good old charge at least some, right? And surely magnetism, though it might take so much it'd mess up other aspects of our device that brought them together.
Heck, I'm just doing basic homework now and had a DUH moment when I realized that wavefunctions (either deBroglie or Schrödinger) have nothing to do with any of the forces we've been talking about, as such. Strictly space-time there -- no EM, no weak, no strong force involved in that math whatever - just a time/space distribution of the matter "wave". Hmmm....so that's not all there is to this, obviously. Well, I have a feeling that learning the math on that latter is still going to be important. Ouch, makes my head hurt when I look at the real stuff, not the oversimplified versions that just say "it's like this, suck it up and use the greek symbol to BS everyone" but the real page by page dense "derivation" and "justifications". Though as Halliday mentions, it's not really a derivation from other stuff, it's a leap of faith entirely, and only is accepted as it matches experiment. There's no way to get directly from classical to Schrödinger by accepted mathematical steps -- you just arbitrarily write an equation that takes the place of what was a single momentum vector in faith and see how it works out, and in this case, it did.
Though not a math hater, things like partial differentials in 4 orthogonal dimensions never were exactly a forte of mine. And that's just the non relativistic derivation, gheesh. I guess we're probably lucky enough not to need the full relativistic version of that.