You do have to kind of teeter the end of the axle upwards as well as rotate the axle shaft slightly to get it into the splines of the differential. I can't say I have ever had any problem doing this, but over the decades I have likely done this thousands of times on various vehicles of similar design full floating axle.
Once you get it into the splines, you should be able to rotate the axle shaft to line up with the hub's studs. Since the transmission isn't installed, you will be able to do the same on the second side, since the differential action of the differential will allow you to rotate the axles independently of each other. It's not so easy if you had a positive traction type differential....on those you would have to rotate the drum to line up the studs.
Good luck...we have all been frustrated at one time or other when something doesn't seem to work like it should. I can't count the times I was frustrated with a job late into the evening, and a good nights sleep seems to solve the problem.
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