Thanks for that. So, yes, that let me generate segwit addresses on the signing machine, but now I'm really confused. The dozen that it generated just now were unique, and not on the lists (as far as i can see) of either of those generated by the online machines. So all three machine are generating (or at least displaying) different lists of segwit addresses.

However, the signing machine did manage to sign a small segwit to segwit test that I did (though these addresses haven't appeared on its list), and has recognised other (at least some) receiving segwit addresses as belonging to my wallets. But not all...