Squeaks in pedal trap work can be deceiving. Sometimes where you think it's eminating from is not where the cause is at all. Some other areas to check are the lyre itself. When using the pedal, the lyre supports could be rubbing in their sockets(polyester finished parts can squeak). The damper pitman dowel it self can squeak when the pedal is depressed(very likely the culprit). The dowel sits above the trap lever in a felt or leather bushed hole, and another bushed hole in the bottom of the damper tray. Have your tech check these places.
Piano supply houses are pretty much the only source for micro-fine powdered teflon in small quantities. There are other sources, but you must purchase in the 10 pound range to start.
If you are working with the pianos trapwork, a bit more than a foot above the floor, that powder is going to get all over your rug, the floor, and any where is it falls on.
Graphite powder has a habit of getting everywhere, and migrating into places you do not want.
The pics you show are probably not the source of the squeak from my experience.