What do I do with a write-up of possibly folklore knowledge?
I could speculate here, but I think you need advice from an expert in that particular field. It may well be that there is journal out there that would gladly publish such a paper, but also the converse may be true. It may also be that there is some special issue coming up where such a paper would be a good fit. However, these things are only known to experts in the field and hence, your best bet would be to contact one. These could be people in your department, editors of journals on this topic, plenary speakers at conferences or authors of books in the field. Knowing this person personally prior to asking would probably be better (but not necessarily so).

If you do not know anybody to contact, you could also look for a journal that seems to fit and write an email to the editor (or a suitable associate editor) with the write-up attached and ask if this would be suited for said journal. It is not uncommon to sound things out that way. (Beware, that a positive reply does not tell much about chances of acceptance.)

If publication in a journal is not important to you or you don't want to risk another frustrating rejection, uploading the thing to the arXiv is the way to go. You get some publicity and some people will read it…