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Must only work on acrylic because I tried it on a plastic enclosure (not sure the material) and it just made a big mess.
VladimirS36, just a hunch. Did you use the focus ring on the laser eye?
Maybe a launch platform stuffed inside the balloon. Some weight would also need to dangle beneath the balloon to keep it upright; maybe some launch mechanics/electronics? A flame would not likely burn inside a helium balloon (and really, you wouldn't want it to; you'd get a large fireball) so a spring-loaded platform with a pointy tip, and the rocket would burst through the top of the balloon, after two seconds fire the first stage. That still only gets you 18-37km into the atmosphere; you need to achieve 160km for low earth orbit. So it'd be a big project.