A sawzall should make quick work of this. If you don't have one and know no one that does, they can be rented. There are also handles that clamp onto hacksaw blades so you sort of have a small, manual sawzall. It will take some work, but you will be able to cut enough that the remainder can be twisted off or chiseled aside.

If done carefully and methodically, a dremel tool can do much of the work without starting a fire. Try to direct the cut so that the sparks are ejected mostly downwards. Stop often and check the area for signs of burning. Have a spray bottle handy to quench any embers, as well as a fire extinguisher just to be safe. When finished cutting, spritz the area with water and check the area frequently for the next hour for any signs of embers developing.

Finally, depending on the finish, cutting and patching the ceiling is not that big a deal, then you can ensure the new box is properly supported instead of relying on the little tabs of the old work box and ceiling material for support.

1 - TURN OFF THE ELECTRICAL SUPPLY, preferably from the breaker, not just the switch.

Those two screws you see protruding from the box are there to hold up the light fixture. Extend these screws to their full length so that they are in the electrical box, but are as long as they can get.

Remove the glass and possibly the lightbulbs from the fixture. You should see two slotted keyhole spaces that should line up with the screws. Push the screws through the insulation and into the big parts of the holes. Rotate the fixture so the screws end up in the slots.

Tighten up the screws, but do not over-tighten. Just tight enough to snug up the fixture to the ceiling.

Reinstall a light bulb, turn on the breaker and test the switch. If it doesn't work, then remove and check to make sure the wires are all attached correctly. They might have jiggled loose during this process.

Reinstall the glass.

There is no adhesive. Don't use any adhesive.