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Here are several thoughts, and I'd love to hear some counterpoints/riffs:
1)
Faith is the source of the cleric's spellcasting power. Divine forces may "mediate" (allow, negate, tamper with) their access to the weave, but the power lies with the cleric. This is how you get factions within a church, and heretics. Even if God A denies you access to the weave, God B may enable it as furthering God B's cause. The cleric can't show, on a spell-by-spell basis, that their power is enabled by their god, because it isn't. THEY are the source of their own power.
(...)
Divination could be made into specific spells PER DEITY. So when you find a scroll, it might be Divination (Odin).
Or it could be that Divination simply comes with a <insert deity name> section. The spell is generic, but you make it unique when you cast it. This would accommodate Druid castings in a clean way.
Anyway, before this gets much longer... thoughts?