Wow, that video makes me cringe. Clearly the driver isn't the one who will be making the repairs.
Well, I am currently building these transmissions for $1750, plush shipping and a $350 core charge (assuming the core is usable it is refunded). This is given the current parts availability
If I make some assumptions about the job I can give you a range of pricing. Assuming to drop the car off at a shop that actually knows something about X1/9s and is competent to do the work; R&R (remove and re-install) labor can run $800~$1000+ depending on the local economy (obviously labor rates vary from places like major California cities to a small town with a low cost of living). Assuming that shop also did the rebuild figure $1000+ in parts, plus labor at $500~$1000. I would think that a reasonable rate for the job would be $2500 to $3500 depending on the parts needed and the local overhead. Parts costs could easily run the price up if the transmission needed more parts than just reverse and I am betting it will. That's pretty much the way I would price it out to a customer and while it that number sounds really high it is legit.
These days I would expect that most shops would either reject the job or price it very high to make sure they cover their butt's if the customer says yes and they find themselves in over their heads. I have bailed out a few shops over the years that found themselves unable to find parts or fix a problem and had to send me the unit to fix.
Thanks, honestly I am debating keeping this car, It kills me so bad this happened. But it did, I'm in the Detroit area, You dont happen to know any shops or people here you could recommend? The guy/shop that worked in this prior to this incident happening has retired/closed.