Some radical ideas:
The Trade Federation is now the Galactic Federation - warlords, not corporations.
The war begins at the end of Episode I and is on-going by the time we reach Episode II.
Instead of voting for a clone army, the senate is voting on whether or not to construct a secret, planet destroying weapon capable of taking out the planets now constructing overwhelming numbers of battle droids. Amidala, for obvious reasons, opposes its construction.
By Episode III, the partially constructed Death Star looms over the Coruscant skyline - an awful reminder of things to come. Now, I don't recall if the Death Star itself is considered a secret weapon or if it is only the plans for the Death Star that are specifically mentioned as being secret, but I'm sure somebody here can remind me.
So, because the war is already on-going, when Obi-Wan and Anakin return from a "border dispute on Antion", it is therefore implied to be one of the conflicts of the war.
When Obi-Wan goes to Kamino, it is therefore no longer a cloning facility. It is a half-way house run by a group of peaceful aliens who care for weary warriors who pass through - the bounty hunter being one of them.
A battalion of Republic troopers also arrived on the planet after being near decimated in a battle in the outer rim. They are preparing to leave again when Obi-Wan arrives.
The removal of the clone soldier concept helps tie it in with the Stormtroopers as recruits concept we see in the OT and also goes some way toward making them more sympathetic (in the Clone Wars cartoon this would be especially useful).
Now, I know what you're thinking - then why is it the "Clone Wars" at all?
Well, I've tried to think of various ways of getting around that. Grievous could be re-cast as a clone of a great warrior of an extinct race (the actual Sith race?), trained by Dooku and Sidious to command the droid armies. His training was so intense and merciless, it left him a Darth Vader like cyborg by the time we reach Episode I. By the time we reach Episode III, he is basically a mechanical husk and has a grudge against Kenobi.
Following from this idea is the idea of replacing Darth Maul with Grievous. How to do this? I'm not sure. Perhaps simply replace Maul's face with a CGI Grievous-like helmet or maybe even rotoscope Maul out entirely and re-shoot his scenes using an entirely new actor and costume.
Like I said, radical ideas.
What do you think?