I can make myself available to address the performance issues anytime within the next few days. It looks like the integrated graphics performance is now great, but it still has trouble with the dedicated GPU. Something about the CPU/GPU handoff because the GPU show 4% utilization and renders frames in a few dozen microseconds (if it could keep that performance up it would be thousands of fps). This may also be related to the 100% CPU utilization issues in other places too. Is there a demo BDX project somewhere? I have IDEA and development software, so I could see if it's something about your game specifically, or if it's a problem with BDX/libGDX/LWJGL. Other games run quite well on this system, so it isn't one of those cases of Apple breaking things.
Yo, that'd be super helpful, thanks! BDX can be downloaded and installed (and comes with a simple demo project) here.
In the meantime, I've updated the demo with a new build with some minor changes. In the latest build, you can press the 1 key to enable and disable the profiler, which shows how much of the CPU and GPU is going to which resources.
If you could take a screenshot of the main menu and the in-game section and post it, that'd be helpful.
It looks like the demo project doesn't come with the profiler enabled. I also seem to be having some trouble with changing the code to enable it and see if the problem exists with the demo project too.