He leaves because he is sick of the infighting, but he just poured additional oil on the fire by betraying his pater's position in the conflict? That seems a bit contradictory. It might make more sense to say that he had failed to understand all the repercussions and personal consequences that would come with the betrayal...
By the time the saga starts, the conflict has been going on for over a decade. Most the the Tribunal is sick and tired of it, and no longer pay attention. Any splash you action may have generated will be of very limited scope outside of your House.
What is it that Bernhard would have heard of Pytheas that would drive him to seek him out? Perhaps a base on good relationship between Bernhard and your mentor? We need a hook of some kind.
As I mentioned, you cannot sail to Helgeland on your own, because Bernhard will only reveal your destination once you're on your way, and after each of you has signed the contract regarding the vis source. He probably directed all of the magi to gather in the city of Anvers (Antwerp).
But yes, if Pytheas wanders along the way and swims around, he will certainly meet trouble of some sort. My problem is in believing that he would survive the trouble he would find, for he is a single magus, far from optimized for survival and/or combat, with a single shield grog. His mix of flaws tell me that if he gets into trouble, he will be quickly over his head.
Another issue is that if he just "swims around" to make his way over to Anvers, then he cannot bring much resources with him. So if he starts out of Fudarus with a good part of the resources he brings, then he needs to transport them. That limits the ways he can travel. We need to find a plausble scenario for that.
I think you're trying too many things in the short period of time available to your magus before the saga starts. So let's concentrate on only a few actions, which will make things more believable. Here a potential roadmap around which you could work.
Pytheas leaves Fudarus with only a few things: the Analects, the Book of Instruction, a bit of silver and his shield grog. His mentor directs him to the ruins of a dead (unnamed) covenant that literally fell into the sea during the Schism War. Exploration occurs, you retreive some stuff (silver, vis, perhaps some other equipment such as an minorly enchanted boat).
But you get into trouble because another magus has claimed the site for his covenant. You can't remain in Normandy nor keep most of what you reteived. You contact a redcap to peddle off some of the things you found. The redcap is Bernhard. Listening to your rants about established covenants, he offers you an opportunity to perhaps form a new covenant. He directs you to Anvers, where you meet the others.
How does that sound to you?