For the past few months, my transmission has been making a constant whining sound that gets louder as I accelerate and softer when the car is coasting. Every so often, I also notice the 1-2 and 2-3 shifts are much firmer (almost a bang) and occur at a higher RPM for a given throttle opening.

The trans fluid and filter were changed two years and 20,000 miles ago. I removed the accessory belt and the whine was still present. Based on some other postings, it seems one solution is to install a shift kit (TransGo) and use Dexron VI instead of Dexron III. Can someone tell me if this would be a viable solution?

When my car made the same whine it was a failed planetary gear in the differential. The shift kit may help the hard shifts, but I suspect the whine will still be there. Give it a try though.