WebKit is in fact the only rendering engine allowed into the App Store, but you have to use Apple's preinstalled version, not your own. Relevant bit:
App Store Review Guidelines §2.17
So it's possible that, if it doesn't qualify as “browsing the web”, you have a chance at getting past that. Some of the most important parts of WebKit on iPhone are also closed source.
The choice to disallow all other web frameworks is honestly a bit odd, but it looks like you might have to do something besides that; it really depends on what you want to change or add from Chromium/WebKit.