I intended to compare our two paths. I had a surprise with your first AIC.
(5)r8c8=(5)r8c45-(5=4)r7c5-(4)r9c6=(4-57)r9c8=(hp57)r8c8r7c9
I see perfectly the logic, no problem, but
1) This is something I am not doing in my solver
2) Using such tools speed up the process compared to my solution limited voluntarily to my level one.
So I stopped the comparison, but I am interested in having an overview of what you are doing in that field