What type of abilities actually work on interrupting the MC's in Phase 3? I see that people say direct interrupts work, but for example, do Monk silences or Fire Mage disorientates work on them?
Only interrupts will work on them. Some silences also have an interrupt component, so those silences will work as interrupts.
Monk ring of peace will work, however your melee might complain about getting disarmed a bit.
Disrupting shout from our warrior tank worked really well for us. Carrion swarm (if you happen to have a demo lock) works too but it doesn't have a lockout so they can begin re-casting almost immediately afterwards.
Any spell that says its an interrupt in its tooltip. Stuns, disorients, etc don't work.