A related datapoint: I redeemed AY points for a one-way BA award ticket NBO-LHR-HEL. I wanted to fly in C and the cost would have been 126k points and €245 in tax & surcharges. However, as there was no business class available on the dates I wanted to travel, I 'had to' redeem a First class award, which came out at 168k points and €296.
That's rather odd the TFC varied from J to F since the exNBO carrier surcharge (and the other elements of TFC) on BA seems to be the same for J and F.