Absolutely do not boil your live rock. Just not worth it when there's other remedies.
Using products to fight aiptasia is pretty crazy because if one stalk exist there's likely others. I hate using that chemical in my coral packed tank. I don't.
I do not know why Peppermint shrimp would die off, as suggested above. As any shrimp they will scavenge throughout the aquarium for food. As long as there is surface area that has algae spores these inverts will live :/ Turn your lights on longer if there's a concern here.
A team of peppermint shrimp would be the best way to eliminate all of the aiptasia including small ones in-between the rocks and plugs we don't see well [yet]. If you have a shrimp eater this kind of sucks... In a 55g tank I would hire a team of 5-8 peppermints depending on the outbreak. They are more comfortable in groups.
A filefish is a good option to get the big ones. Butterfly may eat as well. These guys may pick on polyps or some corals though.. I have a Filefish named "Crusty" I move from client to client every 1-2 months to help me out with the big ones and new clients with them. He's a pal but always has to be removed cause they cause problems w coral.
I like my Mojano wand and laser haha. Peppermint shrimps are way to go imo