I could be wrong, but there is no such thing as factory reman. To be so, they’d have to ship your transmission to the factory in Indiana.i think i ought to go for the factory remanufactured over rebuilt since they replace all the moving parts rather than just the ones that are visibly worn.
Reman is just another word for rebuilt. Many companies take in cores, a guy rebuilds it, and they re-sell it. Some, but not all, transmission shops rebuild it right there themselves, but your shop doesnt because why else would they want to sell you a reman.
look up Jasper and 62te. If you can find a price, thats about what the trans shop pays for it before they mark it up to you.