Naturally, he has a lift to work freely under the car. From what he told me, that he rotated the housing (trans in "N") while he went on to shim between the housing and the transaxle at the opposite side so that the housing would not tilt, and finally it moved out. Hope you will be more successful !
I wonder if the inner groove for the spring ring has a tapered side for the ring to compress.
With regard to the special removal tool, I trust that it might be possible to grind off from the thickness of the fork until it slides in-between housing and transaxle. However, it also might weaken the fork so that it could break off.
The original housing has a ~3/8" wide outer groove cut into it where the boot slides over. Perhaps with a 1/4" wide clamp ring tightened around, into that groove and a puller hooking behind it, the housing could be worked out. Just a guess, may be worth while trying.