I’m assuming you mean an “Always on top” window? Meaning no matter what it will be on top of other windows?
Does this have to be JME? You say it’s a Swing App, so this means you would have to rewrite it in JME unless there’s a Swing to JME converter somewhere… I just looked up “Swing 3D” and I thought swing was just 2D (maybe a 3rd-party library?), so I’m curious if this is already in 3D?
JavaFX, I’m pretty sure, has fixed their issue with “AlwaysOnTop” and it should work.
This issue had been going on FOR YEARS, until some people started getting angry about it, and it finally got done at some point I believe fully.
I had created a clock for myself that was always on top, with some functionality. It also was transparent with a cool image.
Also, since it’s already made in Swing, you should be able to convert it directly to JavaFX(if it’s 2D, Idk about 3D stuff with Swing).
You can create and do some nice 3D stuff in JavaFX, but not sure what it’s limits are.
I figured I would mention this, but @prog’s answer is interesting too 
https://docs.oracle.com/javase/8/javafx/api/javafx/stage/Stage.html
setAlwaysOnTop
public final void setAlwaysOnTop(boolean value)
Sets the value of the property alwaysOnTop.
Property description:
Defines whether this Stage is kept on top of other windows.
If some other window is already always-on-top then the relative order between these windows is unspecified (depends on platform).
There are differences in behavior between applications if a security manager is present. Applications with permissions are allowed to set “always on top” flag on a Stage. In applications without the proper permissions, an attempt to set the flag will be ignored and the property value will be restored to “false”.
The property is read only because it can be changed externally by the underlying platform and therefore must not be bindable.
Default value:
false
Since:
JavaFX 8u20