'96 Ford Taurus Transmission Problem

I have a '96 Ford Taurus with about 86k miles on it that has just developed a transmission problem. It's a V6/3.0L engine. It was a
heavy snow storm not long ago and roads were horrendous, so I had the car in 1st gear going around 20 miles an hour to get through some of the rougher parts. When it was clear and I had the car at a complete stop, I shifted back into drive, and the transmission wasn't too fond of that. It seemed like it lost 2nd gear for the rest of my way home. I could barely get the thing to go 30 mph at about 4000+ rpm's. From then on, the transmission has been spotty. It will hesitate some and other times it will just randomly hard shift gears if it has been driving a while. If I keep driving, then I'll eventually lose 2nd gear again. The problem will be temporarily fixed if I turn the car off for 5 minutes. Occasionally it will take 2-3 retries to turn it back on again because it will stall immediately after starting. If I leave the car overnight, it is fine thus far. It will only start to act up if I've been in rush hour traffic for 45 minutes or so.
For a few weeks prior to this, I had some weird electrical problems. When I put the car in reverse the radio speakers would cut out. The radio would still be on, but the speakers would be silent. That ended up going away, but then switched to intermittently behaving the same way as I drive. I wasn't sure if this could be related or not. Also, the fuel injectors in this thing get gunked up a lot. Every year I have to get them cleaned cleaned or else it will intermittently drum as if a spark plug were misfiring.
Any ideas beyond getting a new tranny? I'll drive it til it dies before I do that.
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