My BCA along with a few other machines run with the cheap polyurethane belt available on ebay, and other retailers I guess.
I join it with an old knife heated with a blowlamp, press the 2 ends either side of the blade and slide them both off together simultaneously to stick together. This does require a bit of practice. The knife only needs to be warm enough to melt the material, I used to get the knife red hot and when the plastic touched it almost seemed to boil, evidently this did not work at all well.
Another thing I have found, if you are trying to repair the initial joint forget it! cut about 10mm either side and start from scratch, same if the new joint doesn't work.
The expensive name brand stuff came with my first BCA and I really struggled to get a good join with it it never seemed to fully adhere to one another, I put this down to being quite old, peoples views above seem to reflect my experience. Also my Alexander D bit grinder came with an old name brand poly belt on it, it subsequently broke, I repaired it (I didn't have any new 4mm stuff so needs must) and it subsequently broke again and whipped me in the chest! (which was quite a painful experience) I doubled up a length of cheap 2mm belt and its still in use today!
I would strongly advise not to use a metal joiner on the BCA, it was designed for an "endless loop" so I would be concerned with wear on the pulleys etc, also I cant seem to find any larger diameter than 5mm, I use 8mm on my BCA it seems to fit nicely in the grooves and only slips when I am using a slitting saw on the lowest rpm( no bad thing really).
I hope that helps
William
As a side note is there anyone here who uses the genuine original belt material? I have one from home and workshop machinery and its too short for my MK3 (it was described as a BCA mk3 original belt) I suspect its from a MK2. Its an odd material that wants to coil it self up because of the way its made.