Honestly, if it is that slow after just a week since clearing the cache you probably need to try setting chrome up over again
I recently went back to my Bionic and I'm using Chrome...
When I first setup Chrome I told it NO for signing in with my google account and I told it NO on all other options to include chrome to phone as well as I disabled google+...
I have no issues with chrome other than it not feeling as fluid as chrome browser for my PC...
My general rule is this: The more freedom you give to an app, such as linking with other apps, linking with web sites, sending anonymous data, collecting location data it doesn't really need or linking with your 'other' accounts generally ends up in something or some function of an app not working properly, slowing down functionality on your device etc etc, let apps have what they need based on what you want them to do and NOTHING MORE.
So try resetting chrome from the beginning, tell it no to everything you can at setup and if you dont use google+ then disable google+ and come back in a week and say thanks or tell me I'm way off
That also helps it not show up as a big battery user in Gsam battery monitor
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