This is my off-the-top-of-my-head idea for putting some mechanics to this idea. I am doing this to more-or-less get an idea of the length of time, as well as accurately represent the struggle it will cause. It isn't meant as the one, or best way to handle this.
It is meant to reflect the fact that the Mage's magic power is tied to their Belief in their Tradition, and as that wavers, so does their power.
The mage has to first "unlearn" the current tradition, and the more entrenched they are in it, the harder that will be, and the longer it will take. Each week, the Mage trying to change traditions rolls current Magic. Each hit on the roll applies a -1 penalty to the Mages Maximum Magic rating, reducing their current to never exceed their adjusted Maximum Magic. This penalty stacks with BGC, if any. This is the culmination of days of work, and Edge can not be spent on the roll.
The Magic Rating isn't actually reduced permanently, but things that rely on a certain Magic rating (like Adept Powers) will have to be reduced to match. Any such reduction will return naturally as the penalty is reduced
If the Maximum Magic Rating is ever reduced below 0, it is counted as 0 and all extra hits are lost.
Once the effective Magic Rating is 0, the Mage can start learning the new Tradition.
To get the first reduction to the Maximum Magic Rating penalty in the new Tradition, the Mage has to make a Arcana + Drain Attribute (of the new Tradition) (5, 1 day) roll.
After that, the Mage can roll current Magic each week, with each hit reducing the penalty to the Maximum Magic Rating by 1.
When the Mage eliminates the Maximum Magic Rating Penalty, they have finally unlearned their old tradition and embraced the new one.