Is there an option for non-oculus vr gear?
You could take the source and check the Godot VR tutorial (https://docs.godotengine.org/en/3.1/tutorials/vr/vr_starter_...) to see if you can modify it for your own headset.
And without hand tracking it may be a bit uncomfortable to do push ups. But maybe the knuckles controller will be comfortable enough.