I would really like to dig up the whole box and start new but there is no where to put the old dirt.
Time to buy yourself one of those compact composters, made of tough plastic (usually black or dark green). They take up hardly any space and will provide you with the best fertilizer in the world. It will take all your kitchen waste (except meat or cheese, which attract rats; eggshells should be baked in the oven, crushed and then added), plus any clippings from your garden or worn-out soil (in fact a sprinkling of soil every couple of inches helps with the decomposition). You can buy a compost 'accelerator', which speeds the process, but it really isn't necessary.
And less garbage to send to the landfill!
PS Trim those roots, brutally. The tree won't mind.