Picture of the Puzzle

Federico Ricci-Tersenghi, Tim Firman, Jon Collins, Joe DeVincentis, and Ken Duisenberg sent solutions

The top corner in the graphic is North-East.  I've also labelled the South-West corner square as (1,1), with the North-West corner being (1,8), as a way to explain where a block is or needs to go.

We first need to get the 112 block lying on the black 112 block at (5,34):
221 to (12,34): N,N,W,N,E,S,S,S,W,S,E,N,N,N,W,N,E,S,S,W
112 to (2,5): N,E,N
221 to (34,45): E,N,N,W,S,E,S
112 to (5,4): E,S,E
221 to (45,56): N,W,N,E,S,E
112 to (5,7): N,N
221 to (34,78): W,N,W,S,E,N
112 to (5,8): W,N,E
221 to (45,56): S,W,N,E,S,E
112 to (5,34): S,S,S
We now need to roll the 112 block to the black 112 block at (8,34).
221 to (67,34): W,N,W,S,E,S,S,S,E,E,N,N,N,W,W,N,E,S,S,S,W,S,E,E,N
112 to (8,34): E,E,E
221 to (78,2): S,W,W,N,E,N,N,W,S,E,E,S,S,S,W,W,W,N,E,S,E,E
111 to (8,5): N,N,N,N
We now need to get the 112 block lying on the black 112 block at (5,78).  Here I'm simply backtracking most of the above moves.  Some of the following moves could be interspersed with the moves for the next section, but I found it easier to think of them separately.
221 to (67,34): W,W,N,W,S,E,E,E,N,N,N,W,W,N,E,S,S,W,S,E,E,N
112 to (5,34): W,W,W
221 to (45,56): S,W,W,N,E,N,N,N,W,S,E,E,S,S,S,W,W,N,N,N,W,N,E,S,E
112 to (5,8): N,N,N
221 to (34,78): W,N,W,S,E,N
112 to (5,7): W,S,E
221 to (45,56): S,W,N,E,S,E
112 to (5,4): S,S
221 to (34,34): W,N,W,S,E,S,S,S,W,N,E
112 to (5,3): W,S,E
221 to (45,56): W,S,E,N,N,N,W,N,E,S,E
112 to (5,78): N,N,N
We now need to get the 221 block to (8,67) to be able to roll the 111 block North:
221 to (8,67): W,N,W,S,E,S,S,S,E,E,N,N,N,W,W,N,E,S,S,W,S,E,E,N,N,N,E
111 to (8,8): N,N,N
221 to (7,78): W,S,S,S,W,W,N,E,N,E,E,N
111 to (5,7): W,W,W,S
Finally, move the 221 block to (56,6) for the last move of the 111 block:
221 to (56,6): S,W,W,N,W,S,E,E,S,S,S,W,W,N,N,N,E
111 to (6,6): S,E

Tim Firman:
Excellent puzzle! Easily the best rolling block puzzle I've seen.

I'm going to use three levels of indent to symbolize the three blocks.
Let a move to the upper right of the GIF be 'U', lower left be 'D',
  lower right be 'R' and upper left be 'L'.
                                                           # moves
L,L,D,L,U,R,R,R,D,R,U,L,L,L,D,L,U,R,R,D                      20
     l,u,l                                     (2x1x1 block)  3
U,L,L,D,R,U,R                                                 7
     u,r,u                                                    3
L,D,L,U,R,U                                                   6
     l,l                                                      2
D,L,D,R,U,L                                                   6
     d,l,u                                                    3
R,R,R,R,U,U,L,L,L,D,D,L,U,R,U                                15
     r,r,r                                                    3
D,R,D,R,U,U,L                                                 7
     u,u,u                                                    3
R,D,D,L,U,L,L,D,R,U,U,R,R,R,D,D,D,L,U,R,U,U                  22
            l,l,l,l                            (1x1x1 block)  4
D,D,L,D,R,U,U,U,L,L,L,D,D,L,D,R,R,U,R,U,U,L,L,L,U            25
            l,l,l                                             3
D,R,R                                                         3
     d,d,d                                                    3
R,D,D,L,U,L,U                                                 7
     l,l,l                                                    3
U,L                                                           2
            d,d                                               2
R,D,D,L,D,R,U,U,R,R,R,D,D,L,L,L,L                            17
     d,r,u                                                    3
R,R,R,R,U,U,L,L,L,D,D,L,U,R,U                                15
     r,r                                                      2
D,R,D,R,U,U,L                                                 7
     u,r,d                                                    3
R,D,D,L,U,L,U                                                 7
     l,l,l                                                    3
D,L,D,R,U,U,R,R,R,D,D,L,L,L,U                                15
            d,r,r,u                                           4
                                                            228 total
I'm not sure if 228 is minimal.

Joe DeVincentis
On the rolling block maze, number the columns and letter the rows so that the
starting positions of the red blocks are A8, H7, and F67.  The solution is
to move the slab so it lies flat at GH56, roll the 2x1x1 three times to make
it stand on end at G4, move the slab to EF45, move the 2x1x1 to D5, move the
slab to DE34 (or CD34), move the 2x1x1 to D2, move the slab to EF12, move the
2x1x1 to D1, move the slab to DE34 (or CD34) again, move the 2x1x1 to lie flat
at D56, move the slab to BC56, roll the 2x1x1 to A56, move the slab to AB7,
roll the small cube to A4, move the slab to A23, roll the small cube to A1,
move the slab to B12, roll the small cube the C1, move the slab to C23,
and roll the small cube to C3.  The slab can get all these places, I think, but
some are a little tricky, and I don't feel like writing out all the moves.
You need to use the 3x4 areas at EFGH123 and EFG5678 to maneuver the slab into
the right "parity" sometimes, and I think you might need to make a loop around
the 2-unit black block in the middle to reach some positions.