Ivan Detkov: It looks like a good set of variants. It proves that L2 is a good move. It is complicated and I am not sure. Could posetcay take a look, please?
posetcay: I checked the moves and they seem to be working, so I added them.
EdIV: L2 works as well. In response to [current position], both G1 adn J1 work. White links up either on the left or the right.
Ivan Detkov: I appeciate your comments but you have to be more explicit. It is not enough just to say "L18 works as well". I will not spend hours trying to solve your riddle and most probably other admins will avoid it either. If you are making a statement like that, prove it.
posetcay: I managed to find a refutation for J2, so K2 is the only accepted move now. Also added a few more sequences to clarify why some moves do not work.
I checked the moves and they seem to be working, so I added them.