I never really liked the relic storylines, there didn't seem to be much backstory behind them. There was some but I desire more :P. Although, I guess implementing it in dynamis would be easier. The way you have it sotek seems a little underpowered. It seems like a savant's tratise +1. Usually relic have something game changing about them from the get go.(besides claustrum Q.Q) For example, Namas arrow and coronach's massive effect on enmity control, catastrophe allowing drks to be self sufficient and not mp sponges. Bravura massive defense down on mob, increasing over all damage of entire party. Gjallhorn, made mp management a thing of the pass when it first came with it's unprecedent amounts of ballad refresh. There are a few weapons that lack special effects like this, IE guttler mandau and excalibur(although i believe this was the best pld dps weapon of the time, that add effect is delicious). But they are still the best damage dealing WEAPONS of there time and even now. Farsha and twastar i believe fail in comparison, well this is what my friends told me at least.
Because the grimoire is not a weapon, as you said comparing it to gjallhorn would be best. And when a bard received gjallhorn back in the day, they where on a whole different level than bards without it. Even know gjallhorn has no equal and they are even thinking of adding massacre elegy(overpowered much?) to gjallhorn. This is why I believed the grimore should do the same thing. Because it is not a weapon, it should enhance an aspect of our job that puts us on a whole different level than the sch's without it. Therefore it becomes something sch wants to work toward. The stratedgem +1 idea is good as it increases our stratedgem frequency by alot, but I feel it needs more. Perhaps:
Augments Light Arts, Augments Dark Arts: Inreases the mp reductions and casting time and recast reduction of the arts. This would help us keep up with blms in terms of elemental celerity and stay ahead of whms in terms of mp effiency. That used to be our big thing back in the day, the most mp efficient job of all the mages.
Or if we want to get crazy. We could put a range elemental weaponskill on the grimoire >.> It would change from a divine magic skill attack to a dark magic skill attack base on the arts that are up. Put our unusued divine skill to the test! It would just appear underneath whatever weaponskills we have with the current equipped weapon. It would be like leaden saulte and wildfire where weapon damage means nothing. Can put those dusty wings to use in voidwatch XD (although mkyrk (can't spell this to save my life) would probably be a better use).
Ok that is enough living in fantasy land hahaha.