You could always just solve the problem with role-playing rather than game mechanics. SR4A already describes something close to this for shamans:
... Hermetic mages typically view their
elementals as servants to be commanded and ordered about, whereas
shamans typically treat spirits as equals—if not gods or venerated
elders—and so implore them for assistance or strike bargains for their
aid (returning the favor with such tasks as ecological cleanup, gardening,
animal tending, worship, and so on).
In practice, this means that shamans pay 500¥ × Force for Binding like everyone else, but their "ritual materials" are gifts for the spirits, service in kind, and so forth. Likewise, your spellweavers could strike bargains with spirits that are equivalent to Binding, but according to the tradition are not "binding." (For a similar example, lots of religious traditions have Spellcasting that is not "spell casting.") Spellweavers should probably avoid the Spell Binding service as a general rule.