I'm the one who commented on the BAT page. I posted on the classifieds page here on Ford Barn about a year ago looking for a Ryan Overdrive, and was contacted by someone with a TRB Overdrive to sell. I purchased the OD and totally rebuilt and improved it. On researching its origins, I traced it to TRB Machine in Michigan. I contacted him and he told me he made 12 of them or so in the late 90s for the Lentville A's.
These ODs are
not synchronized, and are a straight-cut sliding gear transmission. They use gears made for a quick change rear end. Mine (and probably all of them) have a 26% ratio. They shift just like the stock transmission - you must double clutch to downshift it, and time the upshift correctly.
There were a number of issues I had with mine - The speedometer output is in the stock location, meaning it's wrong when you're in OD, so I modified my speedometer output to be on the rear of the torque tube. I re-did the detents on the shifter, as it didn't shift far enough into OD, and it didn't have a neutral position, making downshifting harder. I had to add a washer around the shift rail, because if you shifted too far into OD the splines would bind up and it would be difficult to shift out of OD. The shift rail went into a blind hole, and would bounce because the hole was airtight - I drilled a relief hole. I replaced all bearings & seals as they had gone bad. I also replaced the Allen-head bolts with period looking hex bolts.
After installing it in the car, I'm very happy with it. It shifts like the stock transmission - easy, but you have to time it right and double clutch when downshifting. The 26% ratio is about perfect with the stock rear end. The straight cut gears do cause it to be noisy - it sounds almost like a jet engine, but it's not any louder than the car already is, so it doesn't bother me.