I got a little deep into my animation, and I realized I want to break apart some of the layers such that I can use a Time Offset modifier on a portion to create a loop. The modifier seems to be applied to everything within the Grease Pencil object so I'm hoping there's a way to split things up. It seems Blender has a way to move layers within the same Grease Pencil object but is there a way to move existing layers to a completely new new object?
Select the GP Object in object mode, Press Shift S > Cursor to selected, Shift A > create a new Blank GP object, Shift select the previous GP obj, select the layer you want to extract, in layer menu choose "Copy Layer to selected", press minus key to delete the layer.
Now the layer lies in its own GP object.
Be aware that the Time Offset modifier (as many modifiers) has an "Influence" tab where you can include or exclude one Layer only, so that the extracting operation may be not necessary (you can add more than one Time offset modifier to act on one layer each).