A Verditius weaver can certainly have its place at the covenant.
As for areas of responsibility vs independent stories, both work for me and the saga. Simply let us know what tickles you.
For example, Houlio has staked a claim on the Telsberg family, which are the mundane nobles that "own" the valley.
There are several other locations and themes that anyone can stake a claim on. A reading of the covenants Boons and Hooks is a good place to start. There is also a map of the valley here, which has several sites identified which could provide areas of interest (two abbeys and several villages). There is of course Basel with its redcap inn. Plus any covenant in the three Tribunals that are close enough to take an interest in Tugurium (that's the name of our covenant). Finally, there are several vis sources ideas in this Notes and Claims post. That list is not even complete yet, so if you have additional ideas, add them to the list! 
It wasn't the Tremere that was making me skeptical, it was the part about developping the covenant to make it an important post for the House. That would be met with resistance.