I would just be careful, give the penetrating oil a chance to work, I am not familiar with these drives so it is hard to determine what is causing it to hang up. On the Cobra and also on the Volvo SX which is similar in some respects, if you look at the second pic with the upper gear housing removed, you will see a bearing carrier that has slots for 3 orings. On mine I think that exhaust water would go past the lowest one and there would be salt deposits there that would cause it to be difficult to remove. I tried all kinds of wedges, prybars, etc and nothing was getting it to budge. I realized the only way to safely do this was to put pressure on the strongest parts of the upper gear housing. Given that these new drives do not have a bar going through the upper gear housing, then I'd get 2 pieces of all thread the right diameter to slide into the holes on each side. I looked at the parts diagrams for this drive and the places I could imagine that it might get stuck were the mating faces of the upper and lower, (why a good penetrant may help try Kano Kroil, or Freeze Off) and perhaps some of the gaskets for the water passages as well. There seems to be an o-ring on a bearing housing that it could be stuck on if water can get around this area, the upper and lower may only be sealed with the 2 oring gaskets for water passages. Just make sure every last bolt was removed and if you do use jacks, apply pressure very gradually and evenly. Make sure they do not press on the cav plate for the lower gear housing, that could snap easily.
Heat may work but again be careful, you don't want any area that has bearing seals to get heated up excessively. Is there any movement or flexing at all?