I think you where right in you description of "back to back" sorry :(
you are pushing the inner races apart
as long as the bearing closest to the tool end is tight on the shaft and in the housing I'm guessing all will be well

....now I think about it the inner races shaft and spring washers will all rotate which may be a good reason to go "face to face" because if the washers aren't perfectly central they will cause resonance at high revs

"face to face" would mean the washers don't spin with the shaft as they push against the outer races
that's why I remember "pulling the shaft" so to speak

with the springs between the outer races you need to grip the shaft to hold the tension... in my case I simply used the out runner bell to grip the shaft and hold the tension (not good for your outrunner bearings) what I should have done is add a collar with grub screws, I did have one but I hadn't accounted for the extra room it would take inside the bearing housing

if you don't get what I mean let me know and the next time I'm at home ill take some pictures of mine or knock up a drawing

in a nutshell, instead of pushing the inner races apart from the inside you are pushing them together from the outside

you may suss a better way of doing it ?
let us know how you get on