FWIW my old "The JB Model" does clean up. That's what I immediately noticed and impressed me; which is where I formed my opinion that older ones were somehow 'different' from current production.
Perhaps A5 is just too powerful to clean up well in a wind this robust and A2 is the secret to better cleanup.
Or it might be something as simple as old ones having been wound on the Leesona.
It could also be that in this particular wind rough mags (or even the old smooth black ones) make more difference than one might expect.
Magnet/coil interactions aren't always 100% predictable; and sometimes the results haven't behaved as anticipated.
As with anything else tone-related, certain generalities apply but once the amp is cooking surprises can show up.
I removed my JBs fairly quickly after tryouts; they were a bit too hot compared to my other guitars. But I've read up some on JB swaps.
Of course the discussions are mostly about overall sound or loose lows; for many players cleanup isn't a priority.
Maybe I'll give A2 a try in one someday.
Interestingly, my older JBJ seems to be wound a tad lighter than the more recent ones: 15.7K vs 16.4K & 16.5K for two later versions.
It could just be variance in batches of wire, of course.
Yet I suspect the formula may have been tweaked a little at some point.