A couple days ago, my friend at school got a coloured Guhong. He asked me to solve it for him and I used the new extended cross that I learned. Then I had an idea! I have since been trying to develop my new method for 3x3. It consists of:
1. 2x2x2 block.
2. Extend to 2x2x3 block.
3. Build a 1x1x2 extension onto the side of that block, and also the last cross edge.(at this point it would be like a solved f2l, but without one slot).
4. Use the open slot to intuitively build a fully oriented and permuted LL cross.
5. (this is what I need help on) use the open slot to permute and orient the LL corners, at which point the last slot will solve itself.
I get to solving the LL corners, and then I cannot seem to figure out a way to orient and permute all the corners without messing up the LL cross
I was hoping to make a method that will not use any algorithms, but at this point it looks like algorithms are necessary to finish the last layer.
I was in fact able to "solve" the cube by messing around with the R and U layers for a while, which tells me that there probably aren't too many cases and if there are algorithms they are probably pretty simple, given that they would use only R, U, and F moves.
I do not know if anyone else has come up with this idea, but some probably have.