There is Nautilus and CFL as two of the F2L > LL methods that I've put out there. Below are some additional ideas. Each one can be seen an adaption of various 3x3 methods.
A small change from the current Nautilus F2L style is to solve a stripe next to the first block. This solves the left half of the F and BR centers. Then solve the remainder of the F2L.
FB
Stripe - Solve the slice of the bottom two layers between the BL and R layers. This leaves the U and R layers unsolved. The bottom layer center piece can be either solved during this step or left out. It may be advantageous to solve the bottom layer center piece during the stripe. It simplifies the next step to become 2-gen and allows for easier implementation of corner control and other LL reduction strategies, or for ending the first two layers with a one step last slot as described in the "Advanced Last Slot" section above.
Solve the remainder of the first two layers. It's not necessary but if following the APB steps exactly, the other half of the BR center is filled in then the five pieces of the last slot are solved. If the bottom layer center was left out during the second step, it can be easily solved during this step.
Last layer.
A completely different approach to F2L is to make EIF the default throughout.
FB + Center: Solve a triangle FB on the left and the R layer center. After this step, a neat property is that R r U moves preserve the R layer center. Many 4x4 methods include a step like this, such as Yau, K4, and Meyer.
Centers: Solve the L, and B centers, automatically solving the U center. This is a simple step for two reasons. First, there are just three pieces each for the L and B centers. Second, solving the bottom layer triangle between them is mostly R U to attach it to the end of one of these three piece centers.
L2T: Solve the last two triples using the same Nautilus techniques. Except there is a little more freedom during the first triple and pseudo slotting or multi slotting can be used.
Last Layer
Transferring 3x3 Nautilus to an EIF hold still maintains the "r U* r'" F2L property that is the unique property of the Nautilus solving concept. This means that the steps can be:
FB + R center
2x2x2 pyramid in the back
F2L minus the last slot
Last slot
Last layer