Loosen the capscrews 1-2 turns, leaving them still engaged with their threads and then tap on them. That should open up a gap at the back and start things moving. Work your way around evenly.
Remove capscrews altogether and reinsert from the back, fully engaging with the tapped threads. Go in from the front with a brass punch.
Remove capscrews completely, open jaws until they overhang body and prop up on three pieces of timber. Screw dummy spindle nose into chuck and tap gently on that. That gives a more central application of pressure.
As manufactured, they are a snug fit and as above, petrified lubricant can exacerbate this.
Put some sort of witness mark on the two parts so they go back in the same relative position.