Is it possible for a magus with a way to high lab total using the distraction rule to lower the lab total and so the vis cost for binding a familiar?
So in my example the actual Lab total is 56 but to lab needed to bind the familiar only need 40 so by finish 13 day early the lab total should match the 40 and only cost 8 vis instead of 12?
You magus wishes to handle a situation, of which the authors of ArM5 and its errata apparently have not thought much: binding a familiar below his powers. This is not exactly optimizing your character: he cannot remedy easily in later life the weaknesses his familiar thus incurs.
That said, the method you propose should work well, and help you around the weird phrasing of the vis cost for binding familiars.
Cheers
The situation did arise because our group decided during pre game we go with the limit of Might 15 given in RoP:M 34 for a familiar combined with a bit more complex pre game creation rules for magus then default ArM5.
But even during normal game play I'm sure such situation would be arise as it shouldn't be to unusual that the familiar you find from a adventure or search not full use up the lab total you can provide given the requirements for a familiar.
And thanks for your opinion on this One Shot.
Magi can cast spells with "forceless" casting, ie so they have zero Penetration to avoid accidentally scrying on Magi.
That is a case of deliberately lowering one's Casting Total.
Thus it should be possible to deliberately lower your Lab Total - the Magus just does not use the "full force" of the magic available to him.
Just as long as the magus chooses the final total at the beginning. Which should be easy for lab work. The counterexample is spont magic, where choosing a final total can't be done before hand. And there are some virtues that indirectly make this point.