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^^The Super T10 is a standard tranny and any shop can rebuild it for ~$500 or so. If you pull it for any reason, have that thing gone through.....The shift forks get worn and sometimes cannot be filled with copper to make up what is worn off....but they can be reached through the panel on the side.....
The (Super based) T10 is a pretty stout transmission. I'd be surprised to see damage there. Although, to be honest, I did find pieces of counter shaft thrust bearing (installed backwards by the factory) in mine. I would drain (change) the trans oil and see what comes out. More than likely it's never been changed and it might direct you to the source of the noise.
Oh ya, whirring noise with the OD off is the input bearing to the OverDrive (going bad). When the OD is engaged the noise will stop because pressure it applied to the input shaft, IIRC.
Last year my OD had a wiring failure. Wires to it deteriorated and shorted to eacjh other I believe. that wasw repaired easily. During that failure the light on dash would go out when it failed.
this year it is failing under load when I am traversing a hill at 65 mph. I jumps in and out like 5 times oper second. then I disengauge it and reengage afet I am on a level road. I just had the fluid changed an on magnet there was a considerable amount of filings.
126K on unit. Original.
What would I expect to pay for a exchage from above sources?
Look on the bay. I got a low mile 88 unit (which is the best of the Nash units) for 500 bucks. I see them occasionally in the parts section of the forum as well. There are a lot of them laying around, as they are the redheaded step child of the corvette transmission world.
http://www.ebay.com/itm/84-88-CORVETTE-C4-4-3-AUTOMATIC-TRANSMISSION-OVERDRIVE-SERVICE-TOOLS-STARRETT-/121087915325?pt=Motors_Automotive_Tools&hash=item1c3166f53d&vxp=mtr
I haven't seen this book but hopefully it's better than the FSM..
http://www.ebay.com/itm/Corvette-Doug-Nash-4-3-Overdrive-Corvette-Manual-/220840172540?pt=Motorcycles_Parts_Accessories&hash=item336b199bfc&vxp=mtr