I had a Baum available when I did this job. Its removes and installs. For the install, one side went in from the rear of the subframe towards the back of the car, the other and it would just start to go in at an angle (twice) - so I installed it from towards the front of the car. It was a tight fit. My
regular' mechanic told me (he does not have the tooll) he cuts the outer sheetmetal so it will compress a bit, then drives it in with a hammer.
The shop manual specifically mentions a procedure for 'squaring' up the diff. using a special jig. I am not sure what happens if this is not followed, but I carefully installed the bushings to the same position of the old ones. Not sure if an air hammer would give you this precision.
I used an air hammer to help remove my support joints. In that case, the Baum tool I had available wouldn't work either - at first. I used an air hammer on them (which didn't move them any noticable distance), but it must have freed up a 'bond' because then the Baum tool did its job and the joint pressed out.
I hope my indirect experiences are of some help.