Mushrooms, rics, xenia, and a bunch of other softys cant be superglued to anything directly. The tissue the glue bonds with dies in a couple days and falls off, detaching the animal with it.
If you tank is solid, slice the mushroom up like a pizza and toss the pieces in a place with the lowest flow possible on crushed coral substrate. Sometimes that requires setting a little cup in the tank with 1/2" of clean crushed coral. After about 2 weeks, you will have 6-8 little mushrooms each attached to a piece of crushed coral. Glue JUST the rock to anywhere you want mushrooms.
For the ric, I would go with Nikki's bridal veil suggestion. Stick it where you want it (for ric, you wana give it maxium light possible, so up high), then stretch out the bridal veil over the top and rubber band things in place. A ric can stick in just a day if its happy, but it could take a week or more if its disgruntled.
If you dont feel confident about your water quality, you can use the same method to attach the mushroom, but you only end up with 1 mushroom.
*EDIT* You replied while I was typeing. Very interesting that you have tried the netting unsucessfully. I think there are 2 good possibilitys. First, I think its possible that when you glued them you burned there feet off so they dont have anything left to attach with (fairly common) or second your tank isnt a healthy enough enviroment to promote growth and health. I hope in the shot glasses they have crushed coral in the bottom so they can be trying to attach to something.