I've tried to answer each point in order, with it's own related notes.
Performance: My opinion is that JNI would be the winner here, but I could be wrong, because Jython could be JITed as well.
Easy to Implement: I am taking this as you mean easy to consume the library? That would depend entirely on how you build the API, 1 to 1 method calls, object handles, etc.
Reliability: Jython is the clear winner here, because there is no room for error when you merely instantiate POJOs/ directly access the API right in the client code.
Development Speed: JNI can be very tedious. You are essentially learning CPython modules, C, Python extensions, JNI and then referencing an existing API built in Java.
All in all, if you can make the jump, I think you'd get more benefit in the short term embedding Jython, mostly because there you can directly manipulate the API. I have personally embedded IronPython in a .NET codebase with good success. Yes you lose native speed, but the tradeoffs are hard to justify with the amount of C coding needed for a working JNI bridge. That said, you may well find projects like the one you listed (Jpype) that can do much of the legwork for you.
I would be asking what features of a native CPython runtime I need that you lose when going to Jython. Is your existing codebase in CPython heavily reliant on CPython native features?
Anyway, there's my attempt at an answer.