I know that you have done some of the list below, so I apologise for my repeats, but I would go through the following simple things before moving onto to the carbs
Re torque the heads, the check the tappets – 10 and 20
Take the tank off and drain - swill it out
Take the petcocks off and clean - make sure the mesh filters and reserve tubes etc., are OK - use compressed air
Use new petrol
Check the air filter
Check the plugs
Clean out the float bowls and make sure the gaskets are OK
Blow out the jets etc with compressed air
Check that the choke cables are seated properly - and that the springs are OK, (i.e. are working)
Check that the throttle cable(s) is not kinked under the tank and that the springs are OK
Get the Bike running at say 1200 rpm + and sync both sides - by ear
Run some Redex, (in the petrol), through the carbs
Check for air leaks around the carbs – tighten the clips then use WD40 once you have the Bike running
Test the coil - use a simple multimeter - The book says the resistance on the primary should be 1.15 to 1.32 ohms - and on the secondary 7.5 to 9.15 ohms - You can check these with the coil on or off the Bike – I always take the coil off
Check the HT wires on the plugs – if you do not have a new set – just swop them over and see if there is any change – it may indicate that one is faulty
Check all electrical connections under the tank etc. - take off and clean - a little emery paper - then wipe with thinners and re Vaseline
Check all "earths" - and clean
Ignition trigger - A/R sticking - Bean can - just check that it moves OK - i.e. that it is working - disconnect the battery before you take the alternator cover off
Check the timing – just do the static to start with
Then start on the carbs
Good luck
PS - after each "stage" try starting the Bike and see if there is any change