sounds like you have a parts swapper rather than a mechanic. When a Honda prosmatic autobox goes into limp mode it gets stuck in 2nd gear - it doesnt do the rev/slip like you mention.
The rev/slip is either
1 - the first ratio input pack is slipping (bad piston seals)
2 - stuck lube/pressure valve or clogged oil filter (highly likely)
in either case any sensor can be tested and so can solenoids, all you need is a cheap scope to see whats going on. Honda provide this data as service manual literature.
Alternator replacement warranting idle adjustment is usually when someone has monkeyed with the idle screw on a bad alternator (this is favorite past time of Pk mechanics as "race setting") - Honda forbid it as this engine has an idle speed control motor - but alas as we know in engineering, if you create an idiot proof thing the world will produce a bigger idiot.
You should also look into the grounding point of the transmission, a lot of bad things happen if the ground is bad, This is universal across Hondas entire range, all the way from a small 3 cyl car to a v6 engine luxury car.
I never advise to replace an older Honda auto from the scrapyard as its literally a blind gamble. And if you keep on driving it you will kill the transmission very quickly.
Another point is that whenever you replace the automatic box you have reverse flush the cooler unit as it traps a lot of debris in it which will get pushed into the replacement gearbox if you dont clean it out.
