[PHMCS]

hmm might I trouble you for a bit more info?

it sounds like your bike had seen better days given the repairs you did, so it is possible that the coils and such could be in need of replacement. Even not, if they look iffy, may as well. You can usually nab some used ones cheap if you need some to test against. you mentioned that you tested them for spark - how so? Have you checked to make sure the wire that plugs into the boot is securely seated? Are the plugs you installed CR7HSA and old ones CR8HSA from NGK?

spark issue aside, you may have multiple issues, including fueling (like how it ran til it warmed up then died). a few things to ask about/check:

-is there an external fuel filter? if so, if the pipe kinked and killing flow?
-if there is no external filter, are the little inline filters there? if so, what condition are they in? if not, blockage in fuel supply channel is possible.
-what is the quality of the fuel in the tank like? old, new, rusty, etc.
-given the status of the idle screws, do you know if the carb is using stock jets? if its vastly over-rich or ultra lean, it will have issues igniting, and that would get better/worse depending on which, as it warms up, and p.owner may have been trying to compensate.
-when you cleaned the carb, was the float height verified when putting everything together? this can have an impact on rich/lean.
-are all the vacuum lines in good shape and properly secured?
-is the small hose to the decel valve connected?

we might be able to start narrowing things down with more information.

To answer your other question, while all of them may not be, I also have an 07, and her carbs are unbelievably temperamental.