http://eclecticproducts.com/products/e6000/lists several package varieties of e6000 product. E.g., "E6000 Jewelry & Bead gives you the control you need for precise, no-mess applications. The applicator tips are perfect for permanently bonding stones, gems, beads and most types of jewelry metals." I assume that means the applicator tips are small.
It does not say it works with clothing, but
Not recommended for any items that come into contact with food, drinking water or animals. Do not dry clean.
suggests it might. Do your Synchro dresses need to be dry cleaned?
Also,
Fully cured adhesive can withstand temperatures from -40 to 180 °F (-40 to 82 °C) intermittently.
According to,
https://www.hunker.com/12003256/the-maximum-temperature-for-a-clothes-dryerthat would work with home drier temperatures.
But you won't know til you try. It would be awful if it didn't work, and messed up your outfits. Could you try it on a patch of the same material first?
Rule 9022 in the USFS[A] rulebook, which pertains to Synchro, says
Sequins, rhinestones or jeweled trim may be used in moderation on the clothing of senior, junior and collegiate synchronized
skating teams only (see rule 9021 (E)). This adornment is allowed on the bodice only and must be non-detachable. Sleeves
and skirts are to be void of adornment. Feathers or other materials that could be dislodged upon contact are not allowed.
The use of adornments at all other levels is prohibited. If any part of the costume or decoration falls on the ice during a
competition, the team will be penalized by a deduction. See rule 9923.
There sure are a lot of limitations. But how much would they really penalize you for a few shiny things that fall on the ice? From posts on this forum, it sounds like that is pretty common.