I think June is the sweet spot for the Norte. The weather is likely to be less rainy than spring and tourists are not yet there in droves. If you are looking for non-albergue options, the Norte is for you. Since it goes through so many tourist destinations, there are tons of private options. And in June, since the high tourist season has not yet arrived, we were able to snag lots of good accommodations that would be way more expensive and way harder to book in August. I remember several different two bedroom apartments in beach towns for 60 €. Our group of two men and two women fit perfectly.
I last walked the Norte at age 67, so I think it is perfectly do-able since it sounds like you are in good shape.
I don’t know how much you suffer on asphalt, but my first Norte years ago was almost ruined by the constant pavement pounding. There is a LOT of asphalt, frequently along highways, while the ocean and coastline paths are just a km or so away.
This thread offers a lot of alternatives, and I would highly recommend them, but a GPS is probably necessary. Not that it’s hard to follow the coast, but getting from the camino out to the path on the coast will not be marked or intuitive.
Your stages can be pretty much the same as if you walked the “official” route, but veering off to the coast and getting off the pavement made my second Norte much more wonderful.