I did a re-attachment today, in which I had the same gooey mess (I also left the piece on for too long). I did 3 things differently this time than all the other times and I got my piece pretty clean. Yes even non-sticky to the touch!

1) After taking it off, I put 99% alcohol on the goo, then did a mirror slide (where you slide your piece on a mirror, smearing the goo onto the mirror, then clean up the mirror afterwards. I kept smearing the goo on the mirror until I couldn't feel anymore stickiness on the piece.

2) I then sprayed the piece with Dissolvit ("dissolve it") to ensure I dissolve any thin layer of goo I had missed. Not sure this step is necessary though.

3) I left the piece to soak in the sink with shampoo on it, while I showered (so 15 minutes).

After I got out of the shower, I rinsed the shampoo off the piece, and blow dried the lace. It was the cleanest I've gotten it.
**Don't put water on goo, it just makes it worse. Alcohol seems to clump the goo together, so when I smear it on the mirror, they clump and smear off.

Try these steps, and see if it works for you. Good luck!

Leamon