An idea for AOTC:
Establish in the opening crawl of AOTC that the events of TPM and the sub sequential fall of Nute Gunray caused the Trade Federation to crumble and sparked a civil war. Furthermore republic forces, lead by the former Jedi Count Dooku, have been tasked to settle the conflict. The footage from the Battle of Geonosis could be used to show Dookus crusade, maybe in a montage or something.

Now here comes the actual clue, tell that the Clone Army has been ordered by former members of Trade Federation. This resolves the mystery around their creation and prevents any more investigation by the Jedi due to urge to weaken the enemy, by snatching their army.
Disconnecting the clones from the republic army, shown prior in the edit, should be doable, because there are actually just 2 shots of the Clones wearing their armor while on Kamino.

To top things off, Dookus alliance with the the separatist could be hidden until after Obi-Wan got captured, and played as a twist when Anakin and Padme go to Geonosis (which would now be a warzone) to rescue Obi-Wan and seek out Dooku for help. Dookus turn would sort off mirror Landos in Empire and especially the deleted scene where Padme tries o bargain with Dooku would fit perfectly, albeit some adjustments would be necessary.

What do you think?