Thank you very much for the idea and the link.

I've tested it and it seems to do the job wonderfully. At least on the web page it seems to obtain the expected address.
Too bad I cannot fully test it offline for my exact use case because I couldn't convince monero-wallet-cli accept the seed words in offline mode.
Doing the same with a newly generated seed and the GUI Monero wallet (online) works though.

So indeed, I am confident that for my use case this was the missing bit.