I agree. That's an ugly stump and dead tree. And if you leave them there, they're an invitation to wood ants and such, even termites. If I couldn't do it myself (and at my age, I don't), I'd find a couple of yahoos with shovels and chain saws to dig down and get as much of it out as possible.
And along the lines of what Arico said, I'd leave walking access inside the fence, so you didn't have to wade all the way across the bed to work the far side. If you opt to use the slice and wait method of dealing with the tree, you don't need that space for anything but access anyway. And study your sun lines, so you know the light conditions through the days and seasons.