Agreed. Under-drive pulleys are more to prevent water pump cavitation on high rpm vehicles. I had an under-drive pulley on my RX-7's 9,000 rpm half-bridgeport motor. With the stock pulley, if you revved over 7000 rpm you could watch the temp gauge spike and then crawl back down once the revs dropped.
If you're putting a high load on the engine at a low rpm, i.e. towing, you're going to need a larger cooling system as a buffer. The larger radiator weighs enough to negate some of the gains you'll get from the under-drive pulley.
If the alternator's turning too slowly to charge, the voltage drop to the transmission isn't going to be immediate. The battery's still there, doing battery things, like smoothing the voltage and propping up the voltage if the alternator's weak. Do the automatics wig out if the alternator goes bad? Because the symptoms would be the same.
