Hi
I'm Sreekar, somewhat new freelancer here but have lot of programming experience professionally.
I had the same requirement while I was in college when I wrote a Java Swing UI for a coding competition and needed to wrap it in EXE to make it "click-to-run". I can do your task in 1 day.
I can show you a small demo with a small UI app if needed (just to boost your confidence as I'm some what new)
We basically wrap embedded JRE just like eclipse IDE does and run our application on it.
If you really want a native C++ app for your Java UI program, the budget is not suitable as it is going to be hard task.
Thanks for reading my proposal. Looking forward to hear from you.
-- Sreekar