You might try switching to a non-sticky back stabilizer and use a dissipating spray adhesive, such as Sulky.

Hoop the stabilizer and the set the hoop in a box.  Make a template resembling a frame and set that on top of the hoop, then spray.  This will help contain the over spray as well as keep the hoop glue-free.

"Hi",K,   I went to a Jennie Haskins' conference last week and the representative talked about this very thing.  She said that most wash away stabilizers will have a little residue as they react with the minerals in the water.  So-o, the harder the water, the more the problem.  She said to add Calgon, hair cream rinse, or some other product that will help take the hardness out of the water and the filmy residue will completely disappear as it is supposed to.  She also said to rinse it more than once so that the second rinsing can take out what might be left in the water of the first rinsing.  Good luck with this,  I tried it with a project and it worked well.

To finish my comment - I just made a 'non-knit' yarn scarf using the sticky back wash away.  Very cool!!!