'93 GLX Automatic problems / swap info

I’ll apologize in advance for the length of this post. I’m a firm believer that little details make a problem easier to diagnose.
I bought a ’93 Passat GLX wagon (automatic, 132k) about 5 months ago. When I got it, it had a firm 3-4 shift, but no other problems. The guy I got it from said he took it to an independent VW shop and they diagnosed it as “some kind of solenoid that would cost $400”. I have now put about 12k on the car and it has gotten progressively worse. The 3-4 shift has become very hard, the 2-3 shift has become firm, and when it's cold it shifts at about 4000 rpm. It also will not tolerate any throttle input in 4th gear at highway speed without downshifting. I can maintain speed, but not accelerate at all without it downshifting. When it does downshift, it engages 3rd for about a quarter of a second and then shifts to second. It will hold third only if there is no throttle input, just like 4th. Any attempt to accelerate and I’m in second at 60 mph.
A couple months ago the ‘check engine’ light started coming on in the morning when the car was cold. It comes on for a minute or so and then goes off.
I decided to take the car in to the dealer about a month ago and have them read the codes, since my local auto parts store that usually does it for free can only read OBD II codes. My assumption was that there would be some kind of code related to the transmission problems. The dealer was able to pull three codes, two for the engine, one for the transmission. They are: 00537 011 – Oxygen Sensor Control – Control limit not reached (sporadic DTC), 00533 009 – Idle Air Control Regulation - Adaption limit exceeded (sporadic DTC), 00660 027 – Kickdown Switch / Throttle Position Sensor – Incorrect signal.
The dealer told me that these transmissions are usually bulletproof, when properly maintained, but my transmission fluid was very dark and obviously hadn’t been changed in a very long time. They said they couldn’t give me a definite answer without doing further diagnostic work, which involved dropping the transmission pan and hooking up hoses to do various pressure tests. That process would involve about $250, but based on their experience with transmissions that had the same problems as mine, they were about a 90% sure that I needed a new transmission so there was really no point in taking my money. The service writer suggested that I look around online or in a few junk yards for a used one.
I took the car home and changed the transmission fluid and filter. That was a month ago, and it’s gotten no worse but also gotten no better, with one exception. Last week, after the car had been sitting for a little over 24 hours, I got in it to drive home and it barely turned over (I’ve been having battery problems). The car cranked slowly, and eventually fired, and on the 10 mile drive home it ran perfect. The transmission shifted flawlessly, held every gear, and I was even able to pass a couple people on the highway in 4th gear without it kicking down to second. I put a new battery in it, and all the same problems still exist. Engine light still on, transmission still FUBAR.
Any ideas? Is my transmission really dead? The dealer didn’t seem interested in taking my money, so I have to assume he’s not just telling me this to sell me a new one. Why would the transmission work so well on that one occasion?
Just for kicks, I looked around and found a low mileage 5 speed car in a junk yard. I'm comfortable with the mechanical aspects of this swap, but what about the electrical? Would my computer be looking for a transmission that didn't exist? Would I need to swap the ECU?
Any thoughts on any of this would be very much appreciated.

Conversion to 5-speed would require an ECM change also. If you have access to a complete car try to work out a package price to cover all the little parts you will need.