You get very colourful moths too, [poplar] hawk moths (UK) are large and well coloured; some butterflies and fritillaries are dull hues. I've never noticed moths to be particularly downy though?

Wing position and form is how I'd differentiate them. Moths have a delta form at rest and don't close their wings together vertically?

Well, that's the thing about morphological taxonomy, yeah - it's possible to construct any number of axes of distinction, none of which is really guaranteed to correspond to anything in terms of descent or relatedness. That said, wing posture is imo a better intuition than mine, not least in that you actually can most easily tell dragonflies from damselflies by eye this way - the former hold their wings spread laterally at rest, while the latter fold them along their abdomen. I'm sure there are exceptions in both families, but as a general field rule it does work.

Looking at sources, the current state of play appears to be that butterflies are (mostly) (sorta) monophyletic in Papilionoidea, and moths are paraphyletic in "Lepidoptera except Papilionoidea", but it's all rather messy and nobody's all that sure.

This isn't as unusual as it might sound, actually. You see much the same in Hymenoptera, for example - large insect families just aren't all that comprehensively studied in the first place, not least because many of their members can be quite hard to find, and what prior taxonomic work there was has been undergoing pretty radical revision since the advent of (relatively) inexpensive genomics and the consequent feasibility of molecular taxonomy.