Fazer shows life and directly runs back into its dark hole

[Fazerider]

… So I guess one of my floating needles is jammed which I need to clean.

It may be the O-ring around the body of the metering/float valve. They tend to crack or flake with age so fuel runs round the outside despite the float valve itself sealing OK.
If that’s the case you’ll need to pull the brass insert out and replace the O-ring, a thin smear of red rubber grease (as used for brake seals) will make it easier to reinstall.