I just did my wife's Leggy Outback 4EAT Duty-C solenoid and cluthchpack.
It can be done with the trans in the car. It's not the most fun thing I have ever done.
Drop the exhaust, lower the trans, loosen the driveshaft center carrier, remove the rear driveshaft cover plate.
Then pull the driveshaft out of the transmission. You don't have to remove the shaft from the diff.
Then wrestle off the transfer case. Replace all the parts. The hub that the clutchpack goes into comes out of the transfer case, so you can install it on the transmission (almost impossible to do if you don't remove the hub).
Make sure the parking pawl spring is set, and don't pinch the wires as you install the transfer case.
That's just the basic gist of it.
Like I said, fun stuff.
I don't think they can help you in Japan, but Subarupartsforyou has a convenient kit with all the parts and gaskets.
The shifting issues do not sound like the solenoid, but the torque binding does.