I have tried a few, I have a sps tank with Christmas tree worms, clams, few zoas... until now the only Angel that I found totally reef safe IN MY TANK is an Eibli Angelfish, he has been in the tank for the past 30 days or so and he doesnt touch anything. Always picking stuff from rocks and eats the food I make.
Second close one was a flame Angel that never touched corals nor clams but loved to nibble the Christmas tree worms, he lives now in an sps tank of a friend of mine since I gave him away about one year go.
Sorry, don´t know about a more mixed reef tank with lps corals. Hope someone that has the same fish could chime in.