Hi Kappy, First off top marks for your getting in and getting your hands dirty and not being daunted by the work. I really mean it. Well done. As tough as it is and as super frustrating as it gets sometimes, you are getting some really good experiance in all of this that you can in turn help someone else with.
If I read this right, and if I am understanding things correctly,
She does not want to idle properly and is hard to start especially when cold.
No 3 does not want to fire.
Does #3 fire at higher engine revs?
Checked coils & ignition, plugs etc ... All seem OK.
So going back to the carbs,
Each carby has 2 significant jets ( not counting the needle valve metering) There is the idle or pilot jet and the main jet.
Pilot or Idle Jet below
Main Jet
The idle jet is providing fuel at idle and should continue to provide a small amount of fuel as revs increase. However as the revs do increase the main jet cuts in and provides a higher volumn of fuel needed.
From the symptoms it sort of sounds to me that #3 idle jet is blocked. This would meen at idle it wont fire because it has no fuel feed. Get the revs up and the main jet will provide fuel so it should start to fire but it might be running a liitle lean at revs because its getting slightly less fuel than the other 3 carbys are supplying. It would definatly run like a hairy he goat at idlle and perhaps a tad less than optimum at lower midrange revs and near perfect at high revs.
If this fits the symptoms then I would go back to carby 3 and pull the iddle jet and make sure its clean and can pass fuel.
I had my sons VTR250 fuel go off and foul his carby's. The residual gum blocked his pilot jets. It was tough to clean as well because the holes were small and the gum was very tough. I boiled the jets. And (not advocating this) I used a single steel wire from my wire brush to clean it out. Nothing else would unclog the jets. Sharp steel on fairly soft brass pilot jets is not very good, and I may have reamed the jets in the process but ... it works fine now.