As ever, dsp27 has all the info at hand
I contacted Renaper via DM on Twitter (and they do react much quicker there, by comparison, they answered my question in Whatsapp after 24 hours). They recommended:
1) Desinstale del teléfono la aplicación Mi Argentina.
2) Vuelva a instalarla.
3) Reinicie el equipo y vuelva a ingresar su usuario en Mi Argentina.
4) Siga las indicaciones para instalar el DNI en el celular.
5) Ingrese el código que le enviamos (recuerde que este tiene una validez de 72 horas) AAAA-BBBB-CCCC-DDD.
I should mention that Mi Argentina was available for me on the Apple App Store, even though I'm not in the Argentina region and can't easily change this.
The email they had sent me with the activation code, naturally enough, mentioned none of this. Before I forget,
@Brian_is_here, yes, I had to ask Renaper on Twitter for my new DNI number, which they gave me, and I also had to generate my new CUIL on
https://www.argentina.gob.ar/servicio/solicitar-constancia-de-cuil. The process is online, and I downloaded a PDF with the CUIL.
OK, so to fast-forward through this stream of consciousness account, I input everything into the newly installed Mi Argentina app and I got "Error inesperado, vuelva a intentar mas tarde" when trying to create the account :-( Unfortunately, Renaper deny all responsibility for what happens in the app, and pointed me to
https://twitter.com/innovacionar, who, of course, don't allow DMs, but I did find a link to an online complaint form
https://www.argentina.gob.ar/miargentina/consulta which allowed me to input the details of my problem. Hopefully this saga will have a happy ending, more updates later