I'm reminded of the maxim that the invisible and the non-existent tend to look an awful lot alike.
This is one reason I lean towards anti-realism: it clears away a lot of useless metaphysical kruft that isn't doing any work. Material? Non-material? Who the fuck cares. If it affects experience, it must be accounted for, regardless of its ultimate nature or essence. And if it doesn't affect experience, then you're talking about nothing at all.
First you say these feelings must come from God because they aren't natural. Then you define natural as anything repeatable. Are these feelings consistent and repeatable? If so, you've just defined yourself out of a job.