You can use one of the many headless browsers available. Selenium, phantomjs, phantomjs+casper, webkit, chromium, awesomium, name your poison. All are quite competent in rendering modern web pages. You don’t need to reinvent the wheel.
But essentially on performance, it's comparable to a desktop browser but still slower than I'd like. Java 9 should support HTTP 2 and async HTTP by default, which might help. And I've been looking into short-cutting some of the in-memory rendering but haven't had any breakthroughs yet.
As far as JavaScriptCore engine specifically, it's the default in WebKit so there should be good performance data out there on it.