It looks like that axle is not fully seated. But, the splines would be providing power to the wheel even with it out slightly like that.
Did you use a new clip on the end of the axle? and a good glob of grease on the splines/clip when installing the axle?

To get the axle fully seated:
-use a dead blow plastic mallet
-tap on the axle right next to the tranny at 90 degrees to the insertion direction
-rotate the axle a little bit
-repeat
(eventually the clip works past the jam and snaps into the correct location; I've used this technique installing and removing axles.)

What did you do for your minor overhaul of the tranny?
It sounds like something is wrong with the differential. Not assembled correctly or missing parts.
-drive wheels should not spin independently