I think this is a great route. The forum has lots of info on all of the sections (Baztán, Viejo, Olvidado, Invierno), so it just depends on how much information you want to collect before walking. The Viejo is high on my list, lots of mountains, lots of romanesque, lots of detours.
I’ve walked the Olvidado twice, and though I enjoyed Bilbao to Aguilar, I think there’s no doubt that the route from Aguilar to Ponferrada/Cacabelos is more spectacular, at least if mountains are your thing. But I would definitely take tracks. Not for the Invierno (probably the Iberian peninsula’s most heavily signed camino), but probably for the Baztán, and definitely for the Viejo and Olvidado.
As far as starting date goes, I would start in mid- late May.
Five of us started the Baztán around the 15th and never had anything resembling hot weather. I got on a bus from Pamplona to Irún to try to Norte’s coastal alternatives, but if I am lucky enough to have a next time, I would surely continue onto the Viejo. Summer on the Olvidado is not likely to be scorching, but I would avoid August just because there will be lots of vacationers in the mountains and around some of the attractions.
I know there are several forum members who got the Viejo bug from our virtual planning thread, so you can be sure that you will get enthusiastic responses from anything you post, whether it be questions or comments beforehand, or a live thread.
Buen camino, Laurie