Update: Sorry it took so long. Last week, a trans came up for sale, and I snatched it up as well as a radiator. It took a couple of days to get there and back, then another couple to check the takeout and get it installed. Just finished installing the floor plates yesterday. It seemed fine on visual inspection, and the backlash was in spec. It drives and shifts well.
When I asked about the model number, the fella told me that it was a 3053 on the tag, and not a 3053A. I verified with him over the phone that the shift pattern was correct, and continued on hoping for some kind of discrepancy that would explain the mismatch. I figured if nothing else, I could use it for parts; the price was the same as just two of the parts I would need to repair the old one. When I arrived, we turned it over and the output shaft turned over more in fifth than it did in fourth when shifted in the correct pattern. This is the tag that was on it:
Who knew the Brits made transmissions?
I was surprised that the parts needed are available and only cost about $700. As soon as funds allow, I'll be getting them and reassembling the trans. It doesn't make any sense to just to trash the old one given that all of the other parts seem to be in pretty good shape. I'll post up when it happens.