Thanks for contributing to Parf Edhellen!
I agree that √REN is the way to go for “memory”, but I don’t think this particular neologism would add much. We already have a verb *ren- proposed from this root, that would regularly form a gerund rened “remembering” and the attested noun √RĒNē >rîn “rememberence” that could be used for “memory”.
gilruin
lit. to remember or remembering
Memory comes from the root meaning to remember or remembering.