A problem with any or all of the things you mention can contribute to hard starting. I would look first to the things that have changed since the last time it ran.
Are you sure there is no spark? It is easy to test for. Remove one spark plug, put it back in the cap and lay it on the engine so that the metal part of the plug is touching metal. Lay it as far away from the spark plug hole as you can, in case some fuel gets blown out. Press the starter button and look for a healthy spark.
Check the valve lash and adjust as necessary. You will not be able to properly adjust the carbs if the valve lash is way out of spec.
When the carbs were cleaned, were they completely disassembled? Was every tiny passageway carefully cleaned? The pilot circuit has very tiny passageways that can be very easily clogged. Were the throttle plates bench synchronized and was the fuel level properly checked?
New batteries can be bad. The battery needs to be tested under load. A simple way to do that is to hook your meter up to the battery terminals, not on the cables. With everything on the bike off, note the voltage. With the meter still attached, turn the ignition on and press the starter button. If the reading drops into single digits, the battery is too weak.
The coil can be easily checked. The factory service manual shows the procedure and the readings you should see.
Check under the Articles tab on KZR to see if the manual for your exact year and model is available. They are in pdf format and are free.
