..because Kyuubi restored his Chakra, exactly.
Everything you just listed does not change the fact that he received 2.5 stamina points in all three databooks. If anything, those points are reflecting improvement in Chakra control or the change of dimension Kishimoto thinks in when it comes to power-levels; nothing significant enough to justify such a drastical improvement of his Chakra.
Creating a Kage Bunshin does not immediately spell out Chakra issues. He was worried about it before he created the Bunshin. Because his Chakra was already depleted, using Kage Bunshin would be devastating; for the same reason Hiruzen refrained from using Kage Bunshin against Orochimaru, in the beginning. However, going by your interpretation of that statement, you believe that Kakashi did everything since chapter 568 with half of his Chakra? Alright, yeah.
Oh, please. xd
Now you're saying that he had his chakra restored BEFORE chapter 609?! Now, any evidence of that? Because there's not even a hint, yet alone proof.
Also, nope - he got 3 in stamina in every data booklet.
Even if only his chakra control got better, the effect is the same - he can spam techniques more frequently, INCLUDING Kamui.
Kakashi was worried about his chakra before creating a bunshin, but he obviously was worried due to KB jutsu he was about to perform. :| This can't really be understood in any other way, so I don't get where you got this argument.
However, going by your interpretation of that statement, you believe that Kakashi did everything since chapter 568 with half of his Chakra? Alright, yeah.
Because this is true, geez.
-Kakashi wasting chakra on swordsmen - less than full chakra remaining
-Kakashi performing a kage bunshin, so the remaining chakra is split in half - less than half of chakra remaining
-Kakashi WAS NOT restored by Kurama, because:
a) there was no indication of that
b) it was Naruto with Kurama's cloak, not Kurama himself - and as Kyuubi stated, Naruto cannot give people chakra