Fixing "Unfortunately, the process com.andriod.systemui has stopped" causes a different error.

I read through the detail of previous answers to correct the above UI error and found that uninstalling Google updates allows me to again hold the "Home" button of my Galaxy S3 down to see and/or close running apps. However, I don't seem to have the option to uninstall just the latest Google update as some fixes recommend - I have to uninstall all updates. Then I get "Unfortunately, com.google.android.googlequicksearchbox has stopped" message and I can't do Google searches at all on my phone. Now what??

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