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...quite a few of those allow for AOT compilation to native code

Do you know of any good and free ahead-of-time Java compilers that produce native binaries without any additional dependencies?

I haven't been able to find any, but perhaps my Google-fu is weak. gcj is obviously not a good answer.

gcj is dead.

For good ones I only know of commercial like Aonix, Websphere Real Time, Excelsior JET, JamaicaVM and a few others.

If you want to go free and are happy just with GNU/Linux and Mac OS X/iOS, then RoboVM might be an option.

If you want to go research, there is Graal/SubstrateVM from Oracle Labs and JikesRVM, a meta-circular JVM.