Are you sure the bearing has not already bottomed out on the axle?. There will be quite a bit of clear area between the bearing and race that will come together once you install the assembly into the axle housing.
I presume we are supposed to apply force to the inner race;
YES
While we are talking about driving the bearing on by striking the inner race once the bearing bottoms out there will be a different distinct should sound.
Is it possible to use the big nut to squeeze it back on the axle?
I have made the comment about the ones I have done the bearing pressed off easy, how easy did your bearing press off. If the bearing came odd easy I spec the nut would push the bearing back on. How safe this technique would be would depend on how much the nut threaded on before it made contact with the bearing.
All this seams rather easy to me and others as we have performed this type of activity 100's of times so I understand some of your issues. I will look for a video.
Bearing install
@8:27 this one is on the hard side of coming off. The Pop and the squeaking tips me off to that, its not bad bad but on the hard side.
@23:00 his technique to install the BRG. If in doubt put the axle in a press and finish the job up there I have BTDT.
@27:50 this is what I am taking about bearing race clearance to hub before install.