I have switched from WHM to SCH as main.
Keep in mind healing a tank isn't just about YOU, it is also about the tanks gear. If the snakes hit 5+ stacks you're party is taking WAY to long to down it. Could be because of your method on t1 we always take the main snake to 5-10% then completely switch DDs and burn the second. Our warrior experience with healing says you should have about equal gear to your healer to your tank.

I put eos on the platform behind or beside the warrior tank. Rouse when available. I throw eye for an eye on the Warrior tank right at the split, virus, and aldo. Usually its cool down before 3-4 stacks hit. I psy to fill his HP then adlo then top him off. The only time I feel myself pressing lus is if his hp drops dangerously low and this happens at about 4-5 stacks. His healing buff should help keep him stay at max hp and help your healing. You should be Psy spamming basically. If I have the time I use sacred soil. Mitigation is YOUR ultimate tool.