Is it possible to presurize significantly above ground pressure (to the point of the cargo door departing in an explosive way?!)
No idea about the Gulfs ("they" won´t let me play with really sophisticated toys), but on the Sovereign I fly since 2007 we had 4 (!!) SBs to make the freezing over of a moisture trap in the air / press control system go away. This blockade would leave the outflow valves without the required air to open - so when you start the APU with doors closed, the moment you push the bleed air on button, the cabin pressurizes. At least two sovereigns had their doors blown off this way. (or rather when the crews opened the doors) I had the cabin valves not opening twice, both times when the airplane was overnighting in Helsinki in really freezing temperatures. Fortunately we had read about the misfortunes of a Citation shares pilot (IIRC) who had left his airplane together with the door with the same problem when he tried to sort it out by opening the main door instead of switching off the bleed air... thats why we always start our APU with an open door or an open cockpit window.
I had an O-ring in the damper go awol on a King Air 200 once, so that the door came down with force, I consider myself not being "underpowered" and I JUST managed to stop the door with all the strength I could muster - and I had both arms free at the occasion.