engine looks great!
as for the axle, there are two things that come to mind and have been succesful in the past. OK, 3.
First, you can use a big steeply wedge shaped chisel and wedge it in between the axle cup and the transmission housing, then smack the end of the chisel with a hammer a few times. This has rarely failed me, even on old mid 90s Mazda trannies that are no, no, notoriously shitty for this.
Secondly, you can take out the other axle and run a strong punch/drift thru the tranny and smack the other end of the offensive axle. This works well too.
or, like I had to do on one of Markes axles once, I had to weld a plate onto his inner axle cup(no boot, no goodies, cleaned of grease), and slide hammer it out. Fuckin thing... I had to re weld it several times, as it kept breaking out the metal around the welds on the cup.
The big chisel/wedge works very well tho. In this case, Wedge, you are doing some good back there.