I have four on my Hardinge lathe (different manufacturer - Bijur FSA0 & FSA1), I broke one of the small collet/spacers (like your brass one above, except mine was hardened steel and cracked). I fully understand your use of bad words
Mine have a small felt filter on top of a fine gause. I teased the felt out with a needle cleaned it and replaced it. However, I could not get anything to flow through the things.
A guy on the practicle mechinist site said they are standard parts in the US (i.e. a few dollars). He also suggested that they are pressure sensitve, so that nothing much will flow until the pressure is fairly high (I tried air @ 80psi!). I guess he's right; if the pin is tapered, with enough pressure, it would move and allow a small controlled flow of oil.
If you find a low cost supplier please post here (I will do the same).