I recommend that you bring your credencial from the original SJPdP to Pamplona effort. Start from Pamplona. Use the same credential. Continue where you left off.
Using the same, or an attached new credencial, you can establish that you eventually walked all the way from SJPdP to Santiago. Many pilgrims take multiple years to accomplish the entire
Camino Frances.
This will support a Distance Certificate showing the full distance. Only walking the final 100 Km, from Sarria to Santiago gets you a Compostela. The distance walked before that point on the Frances, or any other route, is irrelevant to the Compostela.
At that time of year, the Norte will likely be colder, wetter and have more snow than the Frances. You can experience snow anywhere in northern Spain at altitudes of 700 meters ASL or more, through late May.
I have had light, but wet snow at Cruz de Ferro in three years there. In 2014, I experienced a brief but intense "white out" at O'Cebriero one morning in late April. These snows were not deep, less than 3 cm. But it is wet and can cover the yellow arrows. THAT makes walking more hazardous.
Taking either route, you will hit a fair amount of rain and mud. But there are more higher peaks and thus more likelihood of snow on the Norte, at least IMHO. Others may disagree.
I have walked the Frances from late April through the end of May twice. I have not yet walked the Norte but have talked to a lot of pilgrims who have done so.
Hope this helps.