You can fiddle with different ways to avoid removing the axles, but
why?  Just be careful with the axle seals as you remove/replace the
axles.  Check them to be sure that the garter springs inside the seals
haven't popped loose and that the seal lips are undamaged before
replaceing the axles.

So.......

Pull the trans out from the bottom (it weighs about as much as a large
truck starter!).  You may want to drain it first and note what kind of
oil came out or check the owner's manual for oil type.  This way you
won't make as much of a mess during removal.  During this operation you
can support the engine with a crane from above to keep it as level as
possible.  After the trans is out, remove remaining items holding the
engine in place, finishing with the front engine support mount.  Pull
engine out the top with your crane.

Toyota MDT in MO