For $150 you can get a Salae LA that will sample to disc, AFAIK the sample size is essentially unlimited, but then you have to analyse the data. I think you can export to various file formats but I've not looked into that.
All you really need to do as far as I can tell is compare one bit against another and count the differences. The actual data doesn't matter. Start and stop bits don't matter. It's just a bit stream and you want to see if it comes out the same way it went in, and if not how many times was it different.
I reckon you could possibly do that,
loop
write bit
wait half bit time
read bit
if <> inc counter
wait half bit time
dec loop counter
either in C or maybe drop to assembler.
Of course with 27 cycles the "wait half bit time" is probably not actually implemented as the loop overhead would about do it.
A Due would have no trouble.
Rob