What do I do with a write-up of possibly folklore knowledge? Some months ago I was trying to wrap my head around some classical constructions in homological algebra. I spent quite a lot of time with this, and decided it was worth it to write it down. I did, it's almost 20 pages, and it's been sitting there in a file since then.

It starts pedagogically enough, reproving well-known results, and then it gets into "surely folklore" territory, i.e. not hard results about well-known objects that I have never seen in print (and I did search quite a bit for them). Then it goes on to prove an auxiliary result which is taken for granted in a recent paper (this was my motivation to do all of this).

It might be hidden in Cartan-Eilenberg (a quite hard to read book nowadays, in my humble opinion), it might not. At any rate, I don't know what to do with this file. Should I forget it? Be happy that I understood all of that, and keep it for personal consultation? Post it in my website? In arXiv? Submit it somewhere? I thought I could try to remove the certainly well-known stuff at the beginning, and only keep the "folklore" stuff; then it could be a less than 10 pages note.

The question is, then, how do I deal with "possibly well-known, possibly unwritten results about some well-known construction"?
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…