Is there room to move the beam closer to the tractor, and attach the 3pt lift a foot or two from the beam end. That might put more between the 3pt arms than there is room, but it would leave the 'work' area available. Just so you can get at the engine to start, adjust, fill with fuel, check oil, and add hyd. fluid, etc.
Thinking something like some of the boom poles, that one end actually attaches to the tractor drawbar, and the 3pt lift arms attach to a yoke coming from around the boom.
Adding counter weights on the front end, with or without the FEL, would also be an option. Doubt you will put more than 300 pounds of wood on the splitter.