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Has anyone ever seen a 3BLD method where you swap edges and corners at the same time?
In the last couple of days I came up with setup moves to PLLs for all the corners and edges.

I used buffers UBL and UB.
After you have done the corners (and the same amount of edges), you will be left with either 4 or 6 edges most of the time. You can solve these with any method you like, but it is easy to do with M2 because I used buffer UB. You can not get parity with this method.

The memo is very different and more difficult than normal memo. Because you need to remember 1 edge and 1 corner for each letter pair.
Maybe the memo will make this method impossible/ very hard to use, I don't know yet.

So has anyone seen any method like this? And if can come up with better setup moves for some cases, please let me know! I am interested in your thoughts about this method.

I doubt I'm the first to com up with this, but layer by layer but the layers are solved in 1x1x3 layers and those layers are solved in 1x1x1 layers. Due to the number of pieces on a cube, this method technically has 27 steps but a lot are naturally skipped.

Step 1: Literally just choose a corner and this step is done
Step 2: Form a 1x1x2 with your chosen corner and an edge
Step 3: Turn the 1x1x2 into a 1x1x3 with another corner
Step 4: Add an edge to the 1x1x3
Step 5: Add the centre to the 1x1x3 with edge
Step 6: 1x2x3
Step 7: A layer with a missing edge and a corner
Step 8: A layer missing a corner
Step 9: A layer
Step 10: Add an edge to your layer (note that the centres don't have to be solved
Step 11: Solve the centre
Step 12: Solve the edge on the opposite side of the centre you just solved
Step 13: This step should already be done
Step 14: I wanna make a joke about solving the core, but I can't think of a good one
Step 15: See step 13
Step 16: F2L minus an edge
Step 17: Solve the remaining centre of F2L
Step 18: And in only 17 steps, we have F2L done
Step 19: Solve a corner in the last layer
Step 20: Solve an edge next to the corner
Step 21: Solve a corner next to that edge
Step 22: Solve an edge next to the 1x1x3 you just made
Step 23: This step should hopefully already be finished
Step 24: At this point, a 1x2x3 will be solved on the top layer
Step 25: Solve one of the remaining corners
Step 26: Solve the remaining edge
Step 27: Solve the final corner

Pros
-6 steps are always skipped
-Many more steps are often skipped
-The first few steps can be solved in very few moves
-Many cubers don't need to learn any new algs

When I solve 4x4, i basically do the centers intuitively. But one day I was solving a 4x4, got the white and yellow centers, partial white cross, and then two middle centers next to each other. Once I get to the last 2 centers, it's pretty hard, beacuse you have to not disturb the other centers. But then I thought, what if there was a way to just do an algorithm to solve those two centers? What if there was a way to recognize a case, then do an algorithm to solve those two centers? For example:
would be r U2 r' U2.
What do you think about it?
Would it speed up your solves?

4x4x4's last two centers are relatively easy to resolve compared to larger cube sizes. I know that there is such a resource available (for more than a decade for sure, probably close to two decades) for the last two centers of 5x5x5. https://cube.garron.us/big_cubes/L2C/

You can just pay attention to the "corner" centers of those images to get algorithms for their corresponding 4x4x4 cases, but the algorithms are almost always going to be longer than if you found the shortest moves for the actual 4x4x4 case.

To some people, "intuitive" means the use of 3-cycle commutators. So, he probably started with commutators and is learning how to solve them the common way (where it's the reverse order for most people).

This is pretty much how I along with every top 4x4 solvers does l2c. It isn’t necessarily memorizing algs as all the cases are super intuitive, but rather over time you start recognizing the case and then just solving it without having to think.

really funny reduction ideas for 3x3
1. Reduce the 3x3 to a Cube in a Cube Pattern and apply the alg that solves the pattern to solve the cube
2. Reduce the 3x3 to a Cube in a Cube in a Cube Pattern and apply the alg that solves the pattern to solve the cube.

Has anyone ever seen a 3BLD method where you swap edges and corners at the same time?
In the last couple of days I came up with setup moves to PLLs for all the corners and edges.

I used buffers UBL and UB.
After you have done the corners (and the same amount of edges), you will be left with either 4 or 6 edges most of the time. You can solve these with any method you like, but it is easy to do with M2 because I used buffer UB. You can not get parity with this method.

The memo is very different and more difficult than normal memo. Because you need to remember 1 edge and 1 corner for each letter pair.
Maybe the memo will make this method impossible/ very hard to use, I don't know yet.

So has anyone seen any method like this? And if can come up with better setup moves for some cases, please let me know! I am interested in your thoughts about this method.

It's a cool idea, but the main problem is that comms are already fast and you're just making life more difficult for yourself in memo (as you pointed out). It's unfortunate because the idea is actually quite fun.