I also love the BK11. Been EDC for many years. Like you, I hate the handle. My solution has been to cover the handle area with JB weld to make it a bit thicker. Looks terrrrrible...
But it works well. The additional thickness makes it easier to use, and it fills the annoying slot at the butt end.
I was going to make an extended handle as you suggest, but I found I really like being able to bash the butt and drive the blade into things. I don't want to give up the full tang.
Next I was considering making a metal handle. Solid scales machined to match the cut-outs of the original. I think that would provide enough strength to mimic a solid tang. I don't hit it all that hard. Usually to punch through light sheet metal like when opening a can etc.
I spent a few hours in a very good knife store looking for a replacement. Could not find a blade I like as much. I have big hands and the BK11 handle is really too small. But the blade makes me keep it EDC.
I will follow the thread with interest.
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...........From Nomad.........Been "on the road" since '97