Thought it'd be appropriate to plug what we're working on here. We're a YC company (W19) are building an iOS browser that's extensible. You can build "extensions" to inject your own JS into pages if they match a certain condition.
I run a Chrome extension that's popular here on HN, called BeeLine Reader. We have an iOS app (and share/action extensions) and have toyed with the idea of building a general-purpose web browser, but we'd much rather be part of an extensible mobile browser. Would love to chat about how you're attacking this problem (and avoiding related App Store prohibitions)!