It's really simple to stop siglint's stone animations as a karok or evie if you have the right setup and are in the right place (timing is not super important)
Karoks: You need to have a cestus equipped and you need 4 SP bars. Simple, when he hops be around the area he lands (or chase after him if it's close enough) and when you can either assume he's going to heal or wait a second to see if he does a lightning attack. If he howls with no circles around him, feel free to use Hulking Fury. The first hit will knock him forward cancelling out his animation.
Evies: 4 SP bars and reverse gravity him when he lands and begins to use his heal (before he turns to stone) hopefully you'll manage to pick him up and cancel out his heal.
Last raid I managed to cancel him 3 times, so it definitely works and if you can pull it off it's much better than sitting on catapults hoping you made it in time.