Crib notes for one half of Rubik's Mate. Ie Rubik's 3x3x3 with a 3x1x1 bandage on one edge.

The outline matches the solution on Jaap's Puzzle Page but the details are different.

Notation

Faces
    L R U D F B (Left, Right, Up, Down, Front, Back)

Slices
    L l  R
    F f B
    U u D

Moves
    <slice>or <slice>' or <slice>2  (clockwise, anticlockwise, 180 degrees resp.)
    Moves are deemed clockwise as viewed from the face specified (so l is viewed from the same position as L).

Outline
Generally the bandaged piece is kept bottom left (at FDL-BDL)
  1. Solve the corners first
  2. Get the correct edge pieces into the slices l and u
  3. Position the centres
  4. Move edge pieces in their slices till they are in the correct position
  5. Flip edge pieces till solved

Sequences

1) Corners
Place the corners FDR and BDR - ad hoc
Then use Sune (defined here http://lar5.com/cube/fas6.html) once or twice to orient the four top corners. When oriented, the top corners are in the correct relative positions.
If necessary twist U until the top corners align with the bottom ones.

2) Edges into slices
Use the corners as reference points not the centres.   
This sequence moves UR to the l slice and UB into the f slice.
U l U' l' U' l U' l' U2
Precede the sequence with moves to get what you want at UR and UB. After the sequence twist R or U to realign the corners.
Repeat till slice l has all its correct edges.

Then reposition the cube so that the u slice is in the l position (bandage still running bottom left)
Repeat with the new l slice leaving the u slice intact.

3) Centres
Perform centre slice moves to get the centres in the correct position. All previous work is undisturbed.

4) Edges to correct position
There are two types of sequence (and all their positional variations) to move edges around their slices.
E1) R2 f2 R2 f2 which swaps the top edges with the bottom edges
E2) R2 f' R2 f' which keeps one edge fixed (UL) and cycles the other three (DR to UR to BL).
Often you will have to twist the bandage (D or L) before the sequence and return it atferwards.
a) start with the f slice
to swap UL and UR:    D U2 f2 U2 f2 D'
to swap UR and DR:   L R2 f2 R2 f2 L'
Perform one or more till all three pieces are correct.
b) l and u slices
The troublesome case is when two adjacent edges in the u slice need swapping and two in the l slice need swapping.
To this end I start by getting FD and BD and also FR and BR into position using E1 and E2 variants. Now if LF is not the correct edge apply this fix (swapping LF with LB and FT with BT):
(U R2, D' f D, R'), (R2 u2 R2 u2), (R, D f' D, R2 U')
The first part places UF and UB at RF and RB, the main part does the swap and the third part returns the pieces to their correct position.

5) Flip edges
This sequence flips UR and all edges in the L slice except UF
(l' U')*4
 
Likewise
This sequence flips UL and all edges in the L slice except UF
(l' U)*4

1