Which pilot jet did you have in there if not a 55/160?
Did the old pilot jet have a hole in the top, like the 55/160 has?
If it's a slot head screw it may have the 55/100 as H pointed out. Meaning it has not had the air feed hole for the idle jet filled with lead shot and then use a different idle jet, such as the 55/160.
So you're saying the tap , when in the Off position, has no problems shutting off fuel. That should rule out the tap
And if the body rocked a little that's not too good.
Ideally you should sort that out with a sheet of glass, some wet n dry and some elbow grease.
Check the fuel line for any signs of leaks from the tap or cracks
Upjet to 120
Replace air filter (with drilled holed), or upjet some more
Wear some earplugs! hahaha
None of that will solve your dodgy float but will get you running better later on.
A quick check to see if the float needle is sealing sufficiently is to take the float assembly, hold it upsidedown and blow through the fuel inlet hole in the centre of the chamber. You'll need to seal where the banjo/fuel pipe fits. The needle should still seal the hole and the float should not move despite you going blue in the face.
Which tap do you have fitted? or is it still stock?