Sounds like your idle jet is blocked. Back firing often means lean mixture.
You can get the jets out without removing the carbies - using a small mirror.
You need to be able to see light through them. Yes, the hole is only fractions of a millimetre....
Carbies often overflow when the 40 year old rubber tip of the float valve needle dries out. Just give the side of the bowl s few whacks with a screw driver handle until it stops dripping. That's easier to monitor with the little overflow hose disconnected at the bowl.
Cheers,
Joe