To save Mayrina, you just have to get someone to the switch and hit it before the cage burns. This can be a matter of luck if the damage Ethel does on her first freebie strike goes badly - she can do a little, or a lot to the cage on the first hit, and that can swing it. If you've got an Astarion or other rogue who can dash three or even four times, you can reach the button right away. If you've got a halfling in your party, you can throw them to the button, though it'll hurt the character a little if you do so. Alternatively, if you're a druid, use alight wild shape (cat for example), and have someone throw that - you'll turn back immediately when you hit the ground, from damage, and be able to hit the button on your turn.
You can also use water to put out the fire so the cage won't burn.
