Major Edit: I just realized the InAppBrowser plugin does NOT fix the keyboard bug alone. I did some more research, and this topic helped. I had to add "height=device-height" to every meta viewport tag. "width=device-width" should fix any problems viewing the site in mobile Safari. The final result is this:
<meta name="viewport" content="initial-scale=1, minimum-scale=1,
maximum-scale=1, user-scalable=0, height=device-height, width=device-width"/>
One of these also had a semicolon thrown in there, so be sure to check and double-check for syntax errors, as they may cause the problem.
If this doesn't work, there is another solution that you might try in place of or in addition to the meta viewport fix. It's several comments down in that topic I linked and involves some changes to the CSS. Changes to this didn't fix anything in my code, but it helped at least one person, so it's worth checking out if you still need a solution.
I tested this fix with iframe and object, and it didn't work--InAppBrowser is still necessary.
/Major Edit.
Here are some workarounds that worked for me:
Use the InAppBrowser plugin. This allows the app to interact with loadstart/loadstop/loaderror events in the loaded page within the InAppBrowser. This is the solution I suggest. However, with iOS 7, you will need to hide the status bar manually, the solution for which is here
OR Load the page using window.location.href = [website url]. If you don't need to worry about interacting with or returning to the app or linking to external sites (both of which I needed), this is the way to go. It's pretty simple, but lacks some of the functionality of the first solution.
OR Get rid of JQTouch. I wasn't able to do this, but much of it is redundant when you're building an app with PhoneGap.