Have you disengaged the transfer case shaft splines yet?
If you have not done this, prying on the transfer case is not a good idea. The transfer case is internally fixed to the transmission here.
A slide hammer is the easiest method. If you look at each output shaft, you will see a threaded hole on the exposed ends. This hole normally uses a special tool that threads in with a slidehammer type handle. Once full engaged in the thread, one good tap of the slide hammer and the splined shafts will disengage the transmission and slide out.
Not having the appropriate tool, the next best thing is going to be to find a spare bolt that threads into the shaft, and bolt a long piece of scrap steel to the shaft. You can then use a mallet to tap the shaft out.
You could also bolt a U shaped bracket or similar onto the shaft, then use a slidehammer with a right-angle attachment to hook the bracket and pull it out.
The shafts use a standard C-clip like you see on most FWD transmissions, but is engaged past the transfer case and into the transmission. Without removing the shafts, you will only be able to get the transfer case about an inch away from the transmission.
THe output shaft removal is not documented... pretty much anywhere. Even the Factory service manuals do not have it, only the technician private manuals are the only places I have seen it referenced. It's not the previous persons fault, they were just going by what they read... you would have to be a Mitsubishi employee or work on that model specifically to know about them.
Be sure to check the large O-ring on the transfer case once it is out... if you gave a decent amount of prying that o-ring and the leading age may have taken a bit of damage. Nothing you can't file down and replace the o-ring with though.
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Good luck with your repair!