0 HP = dust is how I read it, and appearing next to the phylactery "the next day". It's not clear that that implies 24 hours, necessarily. I'd suggest that it happens at a fixed time of day, such as sunrise or sunset.
You should certainly tell me what your phylactery is, where you keep it, what protections it has, and any preparations you make in the event that you need it. It doesn't matter to me whether you keep it with you or the party, or if you build a safe place for it elsewhere.
Which specific PH heroes series powers do you have in mind?
I don't plan to change the rules for immediate interrupts. They do present some unique challenges for
PbP, but with quick posting, I hope we can get by. It would help if you give me an indication of when you're likely to use your interrupt powers, e.g. "use Shield if an attack beats my AC by less than 4" or whatever.