This is a brute force "meet in the middle" solver, working from both the unsolved-cube-state and the solved-cube-state, but with steps. Bottom/left/back corner is fixed. BETA
Any Cube can theoretically be solved in 20 moves. 90% can be solved in 18 moves, but this would take a lot of time and memory. This is an experiment to break this up in steps to get a shortish solution.
Step 1 is solving the corners like the 2x2x2 cube. Step 2 is to make a bar to the bottom left and restrict the number of movements for the rest of the cube. Step 3 is a double bar, step 4 is a block, step 5 is an equator bar to the right. Last step is solving the bandaged cube.