That's bad design then, which admittedly is of no help.
Thinking about it, the whole point of the domed head on coach bolts is that they're supposed to sit proud on the surface not in countersunk holes, If you're going to use countersunk holes you may as well use hex-heads.
Your experience is also something for people to think about when contemplating using coach bolts in countersunk holes.
As both ends are countersunk it would appear as suggested before that your best bet is to try and drill through the heads sufficient to separate the heads and get down through the square section as well. So you can knock them through with a punch. Obviously the separated rings of what remains of the heads won't fall out upwards so you'll have to dig them out, As they're in a recess you can fill the hole with water which will keep things a bit cooler which might help.
michael adams
....