For everybody's convenience, I'm posting the result of a little investigation.
itchtoplay kindly ran a test program I gave him to check how the joysticks were reported to Blastaway. The resulting report was this:
number of devices found: 3
device: 0
analogue axes: 2
digital hats: 0
balls: 0
buttons: 3
not suitable
device: 1
analogue axes: 2
digital hats: 0
balls: 0
buttons: 8
not suitable
device: 2
analogue axes: 2
digital hats: 0
balls: 0
buttons: 10
not suitable
Basically, SDL reports that the shaft of the joysticks is analog, not digital, which explains why they aren't suitable to Blastaway. As discussed in the previous post, the problem originates somewhere between the joysticks and the OS (given that they are treated as analog in the system settings).
Should anyone experience the same problem, I can only suggest to check if the joysticks or the OS offer a way to switch from analog to digital.