Removing a firebox door that is stuck shut

I'm staying with some folks who have a Waterford Stanley Errigal cook stove.  The firebox door has been stuck shut for six years.  The inside of the door appears to be badly warped.  

They can get a new replacement door.  And these are excellent cook stoves, I've used one for a while, so it's worth effort to fix.  The question is how to remove the current one without damaging the stove.  Being a cast iron firebox I don't want to risk cracking it.

It seems unlikely to me, but possible, that removing rust with a penetrating oil, and then heating the door and firebox around it may allow it come free.   See discussion of this here: https://permies.com/t/92396/woodstove-door-handle-rusted-stationary

But if rust is not the only issue, and it is stuck shut from warping due to excessive heat, or we otherwise can't solve it that way, I'm thinking what other options there would be.

My thought was to cut out part of the middle of the door with a grinder, then heat the outer edges of the door and tap on them with a hammer to get them loose, gently enough to not shock and crack the firebox itself.  Any other thoughts?

Interesting problem! I think you're on the right track.

I wonder if the warped door is putting a lot of pressure on the latch mechanism and preventing it from turning. If you remove the knob, is there a way to release or disassemble the latch mechanism from the outside?

I would start by removing the hinge bolts.
Remove the top plate to access the inside of the firebox.
A grinder with a wire wheel to remove as much corrosion as possible.
Penetrating oil from both sides.
Careful tapping from the inside out, vice grips on the knob to help it remember to turn.
Perhaps a skinny wheel to cut the latch free on the inside if the knob refuses to turn.
Real heat such as an oxygen-acetylene torch not to cut but to heat the cast door.

Is the stove warped, as well as the door? It would be good to know if the new door would fit before buying it?

All good ideas here. I personally would remove as much of the corrosion as possible manually and soak it down with a liberal amount of acetone/ATF in a 1:1 ratio. This is the best penetrant that there is if you ask me. If times get hard get out the red wrench (oxy acetylene torch) or even MAP gas and get everything nice and hot, then add the mixture and let it soak overnight.

Nice stove!
How do those hinge pins come out?
I'd try that first if they come out easy, the door should just pull away from the latch.

I wouldn't put acetone on anything hot because of the flammable vapors it would create.

To me that looks more like creosote tar has gummed up the gap between frame and door , the doors dont warp really as they are cast iron ,and the creosote is from a slow smouldering fire ---not much heat to warp ---it might be off set slightly as these are loose fitting , by someone trying to prybar it open , If you can remove the entire stove to outside and use a petrol powered high pressure power washer on it, in my own experience the best dissolvent of creosote tar has been water---no soap at all --just water. Then the really hard burnt creosote could picked away and a rubber mallet used on the door ---might just be enough room to tap outwards---i only would cut and destructive remove the door if i had a replacement door to hand--hard to get usually