That is one good looking w123 turbodiesel. To answer your question, I used a rubber mallet to drive the axle into the splines and once the splines engaged, I relased the pressure on the hydraulic jack so that the weight of the diff forced the axle to straighten out. Put lots of grease or gear oil on the splines to help them slide in the hub. I did replace the seals on each side. The old ones were very difficult to get out. I had to use a crow bar to pry them out. If I knew they would be so stubborn, I would not have replaced them because mine were not leaking. The ID of the seals have a groove for a metal spring energizer instead of an o-ring, so the seal is always good. The old seals were not even worn. Trying to install the new seals was also a task. Small slivers of the rubber did tear off when I installed them. However, I have not noticed any leaks yet. If your seals are not leaking, I would not mess with them.
2001 Dodge Ram 2500 Cummins Turbo Diesel - 4x4, auto, 3.54 gears, long bed
'92 300D 2.5 Turbodiesel - sold
'83 300D Turbodiesel - 4 speed manual/2.88 diff - sold
'87 300D Turbodiesel - sold
'82 300D Turbodiesel - sold