but trying to avoid the manual labour if possible!
I'm not sure that is possible.
I would start by cutting off as many roots as possible with a pair of loppers. As well as removing some weight that will let the soil dry a bit more, or let water in more if you use a pressure washer. Also it will make it easier to see the structure.
Next I would employ a demolition saw to cut off whatever is possible. For mine I use 5TPI and even 3TPI blades that get through wood pretty fast.
There seem to be a lot of thickish roots that can be removed using a demolition saw. More significantly, IMO, there are a lot of, for want of a better word, sub-trunks rather than one massive single trunk. So you may be able to get quite a bit of weight off that way, as well as opening it up more.
In between each lot of cutting I would give it a good few blows with, say, a sledgehammer to knock loose any dirt which is now dry or free.
If you can get the weight down enough to make it moveable then any of the possible ideas (giving away, taking to the dump, burying, etc) become possible / easier.