Rick,
I think you're aware of this, but if the tranny's putting enough heat into the radiator via the tranny cooler to actually overpower your cooling system's capability then the tranny's getting SERIOUSLY hot.
I'd consider a couple things and I'm sure you've attended to them, but I'm mentioning them since even the best of us will make mistakes when under duress.
What's the status of your fan clutch? Your radiator? Are all 4 of your tires same wear/size etc? Does your rear heater work? What does the tranny fluid look/smell like? These are basic things that I'm guessing you've already checked into, but as I said we all tend to ignore the obvious, or make unwarranted assumptions when under pressure.
I don't know how the tranny could be the culprit here, actually, so I'm going to cast some doubt on that. If, for instance, there were debris in the new (rebuilt?) tranny that blocked the tranny cooler then the tranny would indeed get hot, but it would not neccessarily transfer more heat to the cooling system than normal simply due to reduced flow. If you reversed the hoses, again the tranny would get hot but I can't see it transfering more heat to the coolant this way, either. You'd have hot tranny fluid in both cases, but improper flow through the cooler.
So, I'd look to the basics of the cooling system integrity first. Just as an overheated tranny will elevated the coolant temp, a suboptimal cooling system will overheat a tranny. Which one do you have? Dunno, but I feel things point more at your cooling system than the tranny - which seems to be operating correctly, no?
DougM