[ImperialCrown]

I've heard a 'buzzy/reedy' type noise when a splash apron or splash shield starts vibrating in the wind. Once they start, they usually keep vibrating until the vehicle slows to a point where the road draft isn't sufficient to keep it vibrating. They won't really change pitch or volume.
Look for loose or unfastened splash aprons at the front behind the grille, at or under the radiator or at the inner fender area.

 

[ImperialCrown]

Replacing the axle shafts without confirming that the noise is from them would be an expensive guess. If the noise is happening almost all the time now, that could be a good thing as it will make finding it easier.
If you can safely support the vehicle or get some lift time, I would raise the vehicle off the ground. With it running and in gear with the wheels turning, try to pinpoint the noise source.

 

[ImperialCrown]

Also inspect the inner axle stub shaft seal surface finish where it contacts the seal rubber. If it is worn, grooved or dinged, the seal will probably leak ATF again.

 

[ImperialCrown]

In order to get an accurate carrier bearing preload adjustment, the transfer gears and shaft must be removed so you are only measuring only the carrier bearing drag itself. This can't be done easily or accurately with the unit installed in the vehicle and it should be on the bench for this operation. This is the procedure given in the service manual and that would be the shop method.
Shop flat rate times vary by shop. A few calls in your area should yield some numbers.
First confirm that the bearings are really your actual problem or continue on with your noise diagnosis.
If this is truly a 1990 A-604, many improvements have been made since then and a reman would likely be recommended over rebuilding what you have. The latest TCM software is also the best way to go. Evaluate the vehicle's overall condition before deciding on an expensive repair.