2001 Chevy Tracker Coolant in Transmission, is it trash now

At the end of January '10, I noticed there was something up with the radiator. And of course it just went out of warranty. But it was not alarming, just differences in the reserve tank levels and elevated temp readings. At the end of Feb while returning to the office, I let off the gas to coast up to a red light; then it turn green, so I engaged it again.

Only there was no forward movement. The motor revved up but the car did no advance forward. I had enough momentum to pull into a parking lot, and put it in park. I sat for a minute and ran through the gears, taking note of it shifting in and out. I put it back into drive and it took off, but now it would not go out of 1st gear.
Now, this behavior just took place that day with no prior signs or warnings of issues. It was in with a mechanic the week before to get the brakes done and was driven by him with no signs or issues noted. After a while of sitting I then tried it again and it appeared normal, only to repeat the process again after about 5 miles. I checked the transmission fluid all times it happened and was getting odd readings.

I took it to a transmission guy and he stated that the fluid was full of engine coolant and he could get a new one for $3800.00 or rebuild it for $2400.00. He never mentioned any issues with the radiator or getting it fixed.

I figured since the problem had to be due to an issue in the radiator and it explained the reason it had been acting odd, that this would be the place to start. He stated to me that the pan was full of shavings and chunks of metal and on it's way out the door. I asked him if it would be wise to drive it, and he said no problem it would just continue acting the same way.

I decided to pull the pan and fluid at home to inspect it. The magnets were loaded with slurry, pan was filthy, but I found no chunks. And the fluid did not smell extremely burnt or out of sorts, just not normal due to the coolant. So, I figured why not try to replace the radiator and solve that problem then go have the tranny flushed completely after pulling the pan and replacing the filter. Which has never been done to my knowledge.

So my questions are this: Is it the tranny truly lost? Or is my thoughts of fixing the radiator and then flushing the tranny a viable fix to the problem? If no to the first one, and seeing that I am have way complete except for pulling the fluid and replacing the filter and then getting it flushed is there anything else I can do or should consider?

Thanks,
T