I think you are also giving yourself too much credit on the separability of tense and mood and if it does not fit into your mental model you are discarding all other options. You can do the same research yourself. Mood and tense are not always separable as you might think. Morphology is a red herring here. It clearly transmits the essential time information and also adds mood no-confirm structure on top. Hence if you don't consider that as a tense, then I have the same suspicion about your knowledge and obviously I might be also wrong.