what is the best knot used for piecing out logs
other than running bowline

Although not knots but hitches I use Clove, Timber and Cow Hitches always (nearly) with a half hitch on the standing part of the rope in the case of Cow and Clove and a seperate half hitch with a Timber hitch. A webbing sling and a rigging karabiner can be used chokered around the branch but unless there is a sewn or spliced eye in the lowering line a bowline would be a good knot to use to clip the karabiner in as it is easy to undo. A figure of eight on the bight will not reduce the strength of the rope as much but will be hard to undo. For heavy loads ues a bowline on a bight ensuring that both loops are clipped into the karabiner. Running bowline is the best option when the part to be chokered is remote from the climber, i.e. tip roping.