I think this is a great recommendation given your time and objectives. Lots of hills between Irun and Bilbao, taking you through San Sebastian and finishing in Bilbao. There's a lot to like about that.
There are some 'alternative' paths which add even more challenge (and spectacular views) to the usual path - e.g. on the first day, when you climb up to Santuario de Guadalupe, you can choose the 'Alpiniste Way' or a lower path to take you to Pasajes.
I’ve walked to Bilbao three times and it didn't get any easier! Each time it’s taken 6 days but there are accommodation options to make this a day or two longer if you prefer.
If you find you are in Bilbao with days to spare, you can either continue on for a few days (not so hilly from there though), or make your way back in the reverse direction. For example, you can go back from Bilbao to Deba with train/bus and walk back to Irun.
If you decide on the first week of the Norte, my tip is to start from - or at least visit - Hondarribia. The Way is marked from both Irun and Hondarribia and meet up very soon after the start. Hondarribia is an interesting and picturesque town.
A week or so on the Primitivo is also a good recommendation but, just from personal experience, I think it would be harder to 'leave' than tapping out of the Norte after Bilbao. Also my recollection, based on no science, is that the first week or so of the Norte will give you tougher terrain day on day than any week on the Primitivo.
I've also walked the Salvador over 6 days of relatively short distance - of which only 3 days had significant climbing - albeit they were tough days. But, as
@Perambulating Griffin says, there are alternatives which may make it tougher.
I don't know where you are travelling from - but ease of getting in to and out of may be a consideration.
For the first week of the Norte, it's easy to get to Irun from Bayonne / Biarritz or San Sebastian. If you are flying in, the San Sebastian airport is in fact just outside of Hondarribia - so you leave there on foot and take a short walk either to Irun or Hondarribia, depending on where you are starting. Bilbao also has lots of transport options for return.
All just based on my experience and recollections - others may disagree with comparisons. But in any case you are spoilt for choice. Enjoy. xx