Thanks for a nice bulblog with colourful plants
Maybe this will be the chicken teaching the hen to lay eggs but may I suggest that You leave much more of the stem of the tree when cutting down. This will help when removing it.
We have previously cut the trees all the way down to the ground and then excavated around the roots in a quite wide area to be able to also get the central pole root and cut it of.
Now we are cutting i so that we have 2 meter or so of stem to have rope and tile and have the other end around an other three. We can then make the hole smaller and only cut and remove (part of) all the side roots and just dig around the pole root. That is broken by rope and tile As well as leaning and pushing (to make it even quicker. This has made the soil damage less and if it is done when the ground are semi frosen it will be even less. It is then harder to dig so pros and cons to everything.
the root bits going away from the stem is only removed if it is easy or if it is necessary
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This way of cutting down trees saves a lot of work and now we only cut the trees all the way down if we do not want to remove the stump.
Thanks for an interesting theme and maybe others have even better suggestions or ideas views on this.
All the best
Joakim