Hi Alaskangirls
When I planned for the Lebaniego/Vadiniense a few years ago I also looked at whether I might combine some walking with the Picos, but in the end I ruled it out. I think it could be done, but if you did it unguided you'd want to be experienced and capable in the high mountains.
Have a look at Mapy.cz - enter Espinama Cantabria as a location and then select the outdoor map option from top left menu. You'll see that there are a few waymarked paths that can take you north into the central massif of the Picos and also bring you back south eventually to pick up the Vadiniense (although that bit is not so obvious).
A big circuit would be to head north west off the Vad at Cabanes, up to La Quintana (instead of going via Potes). Then head west, where you could even book to stay at the refugio Caseton de Andara before climbing into the high peaks.
A shorter circuit, including Potes and Santo Toribio, would be to come off the Vad at Fuente De - you could even take the cable car up into the mountains. From there you'd find several waymarked routes across to refuges such as Jermosa Collada and Cabana Veronica. Details of all the refuges and booking arrangements can be found here
https://reservarefugios.com/en/shelters
I'd just stress again - this is something I've researched but not done myself, and having been up to the high point on the Vad in late June and observed a lot of snow still in place on the higher peaks around me, I'd not be doing it before late June. Having said that, if you are experienced, and the weather is clear, you could add a couple of unforgettable days in the high mountains to the Vadiniense camino
Cheers, tom