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Simply rotate the medge that needs flipping into the unsolved layer and perform the double edge flip as described above.
Rubik’s Blocks, Original 3x3 Cube with a Twist Challenging
I personally put a random buffer-piece in and then solve it, the thing you want to prevent (hence this comment instead of an answer). While having the exact same mechanism, the Rubik's Cube parts all have the same size but differ from one another with the help of colorful stickers, the Mirror Cube is the exact opposite.All of the Mirror Cube's stickers have the same color (traditionally reflective silver or gold - thus its "mirror" like look) but can be difrenciated by size.
Rubik’s Blocks
The 4 vertical center turns are repeated and the bottom turns repeated, 3 one direction and the 4th one back.If you watch the piece this takes the two of them, splits them rotates them, and aligns them reorientated on the top layer. This takes the two pieces, rotates them to the back, pulls the right side back in place, flips the front for the two pieces, and then rotates them in and flips it down. Then the vertical slice is rotated once more but the bottom slice on the fourth rotation is turned opposite to the previous three times. An intuitive solution is to remove both the corner and edge, splitting them up, then move them back in an intelligent way. This is in fact only one formula, but the others are the inverse and mirror image along the FR-plane.
Cubesolver
The Block's unique mechanism and different sized blocks result in the Cube changing shape with every move you make. This algorithm is especially versatile since it can be modified to accommodate an empty slot in any other position by changing the first and last Ds. This is done to create either 4 flipped edges, in the bottom layer, or 2 flipped edges, opposite one another. My advice is that if you don't have any empty slots, then you might as well continue doing what you're doing. Whatever moves were employed to rotate the flipped medge and position it opposite the flipped bottom edge piece need to be reversed.The algorithm you've provided doesn't address the case listed in the answer above, where every edge is solved except one. Either way, once you learn a more advanced method, the solution to this problem would be to avoid being backed into a corner with this case at all. You now need to rotate the moved middle edge back into the middle slice and in the process the relocated bottom edge back into the lower slice. I rotate the medge piece into the final layer and in the process rotate a placed/oriented piece out of the final layer. If the first 4 bottom slice turns were 3 clockwise and one counterclockwise, the next 4 need to be 3 counterclockwise turns followed by a clockwise one.
Mirror Cube (3x3x3) - Grubiks Online Mirror Cube (3x3x3) - Grubiks
Once the bottom edge pieces are put in place, either one or three edge pieces are flipped, due to the flipped medge. But if you want something that doesn't touch the F2L at all AND is quick to execute, then you'll have a harder time finding them.When only 2 edges need flipping I orient them so they are in the bottom opposite one another, one in the bottom front of the cube, the other at the back. I would suggest starting to look ahead (which you might do earlier than this, but could do here), you know you will want all the top (as you show) edges to have the correct flip, this would be an ideal point at which to start combining your efforts - your method most likely does the corners next, but it is most likely that the manoeuvres you already use do not flip the edges*. A way to solve this is to replace the flipped edge by a random block and then put the edge at its right place.
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