I think the handpieces are pricey because they have become rare.
There's some info about the older Weller products
here. It at least says that the control board is DS1030, though not much info can be found about it. You could however dismantle the unit and reverse engineer the control board, as it is old, it must be simple.
As for modifying a newer iron, the controller for WSP80 doesn't used DC drive but switching the AC from the transformer with a triac. It's also a 24V unit.
The question remains it the type of temperature sensing element, I have no idea if that's compatible.
Are you sure it's the iron and not the controller that's not working?