Or collect dust into an old-fashioned single-address wallet or perhaps into a paper wallet. Would that work better? If so, then the moral could be amended to, "Don't collect dust into a HD wallet."

I can only amplify what you already wrote---if you have a dust-filled HD wallet, i.e. many addresses with a tiny amount each, then check this web page: https://jochen-hoenicke.de/queue/#1w for your chance to get a dust-consolidating transaction confirmed with a very low fee, like 20 satoshi/byte. Then send the transaction and wait, perhaps for up to 3 days, when, in most cases, the transaction will be auto-cancelled. Then you can try again, until you succeed. Weekends often provide a better chance.