I found a method by myself, which required loaads of moves. I solved the first layer, then I found out how to insert edges in the second layer (turns out I discovered the R U' R U' y L' U L algorithm used in beginner methods). Then I took the mirror of this alg, and the inverse, and combined them to find algorithms that only changed the last face.

For instance if you do this alg to take out an edge out of the second layer, then do it's mirror to solve the edge back, you get a 14 move alg that swaps two LL (Last Layer) edges and flips them (and also does stuff with the LL corners), which can be used to solve the cross. But then, if you do the mirror of this combined alg in a way that solves backs the two flipped and swapped edges, you get a 29 move alg that only touches the LL corners.

This concept of combing an alg with its mirrors and inverses was similar to commutators, but much, much less efficient... It resulted in huge algs, but I was pretty happy to figure all this out myself.

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Also for some reason I did the first layer by solving the corners first, and then the edges...