Witeden 2x3x4 Camouflage Cuboid

I posted recently on the Facebook Puzzle Photography page:

From scrambled to almost cuboid took about a half hour. To go from scrambled to solved corners is easy. It took some fiddling and experimenting to get it to almost cuboid shape.

I used 3-cycles to move edges around. Made good progress fairly rapidly but then wandered around in circles near the end. It took an hour and 20 minutes to solve all the edges.

Getting the centers at the end wasn't too hard.

This was my third solve of this puzzle. It was by far the best scramble.

I've had this puzzle for almost a year and made an effort to analyze it months ago but couldn't make enough sense of it to scramble it. Eventually put it away and forgot about it. On the return trip from the CR I got back to it. Since being home I've made good progress in my analysis and have solved it maybe a half dozen times. Here is my approach so far.

1. Solve the Corners like a 2x2x2.
2. Try to get it to cuboid shape.
3. Cycle all the Edges home.
4. Cycle the Centers home.

Step 1 is self explanatory.
Step 3 has two parts. First get the whites and yellows. Use a commutator that goes from one white or yellow piece to a spot that should be to a spot on the side that shouldn't be but is. Or use a commutator that goes from one side edge to one that is white or yellow but shouldn't be, to its home. Use the 3x3x2 corner cycler to put all the non-white/yellow pieces home. Any face can be forward.
Step 4 can be accomplished with a commutator also. I hold 2 on the bottom and one on the top. The one on the top that is the wrong color is in back. The one on the bottom that is the right color is the first one that should be brought to the top. The commutator is a bit different than most:
( Twist D if necessary ) ( r2 U r2 Ui r2 ) ( Twist D one way or the other ) ( r2 U r2 Ui r2 ) ( Twist D if necessary ).

Steps 1, 3, and 4 are becoming somewhat routine now and feeling more and more like most other twisty puzzles in my collection. Step 2 is a big mystery to me at this point. I just keep fiddling with it until I get it, but there is usually some blockage to deal with and I'm not totally sure how I've done it.