Like I said, I get compulsive.
What I ended up with while swatching was a small cotton turtle shell:

Here's the first thing we may have missed: both sets of instructions say "with yarn in back, slip next stitch blah blah blah." Thing is, that only works when you're on the knit side. So, knit side: w/ yarn in back, slip stitch (the way you have been, "purlwise"), move yarn to front, slip stitch back, turn. The yarn will then have to be in the front to purl, so that completes the wrap. On the PURL side, however, you have to start with the yarn in the front, slip the stitch, move yarn to back, slip stitch back, turn. Then the yarn will have to go to the back in order to knit, and that will complete the wrap. You may have been doing this already, but I think I did it wrong on one side or the other on my tank.
Next: pictures!
Wraps that were done on the knit side:

Wraps that were done on the purl side:

How to pick up the wraps on the left side (where they were knit-wraps):
Pick up wrap like so:

Then the stitch itself:

That's the "easy" side, b/c you can see what you're doing.
Purl side:
What it looks like when you start:

Pick up the wrap from the back, like so:

Needle is then set up for inserting into purl stitch:

Getting the yarn through both of them is the trick over here -- just be patient and very slow.
Result: Happy little turtle.

The wraps on the right side of this picture, the ones that you can't really see? They were my second attempt. Even so, the ones on the left are better than the ones in my tank top. :P
Hope that helps! (Me? Compulsive? Never.)