I know you're not asking for opinion, but I think you're restricting yourself too harshly here. Speed run on Proud at level 1 while going for the Unchanging Armor trophy is just nuts. I'm not saying it can't be done, but it has to be very hard and you might only be able to accomplish at most two out of those three goals.
Anyway, on to the question. A sure-fire way to get the Unchanging Armor trophy is to not alter your equipment at all. This means sticking with the Kingdom Key throughout the game and either a) not equipping accessories if you're playing on Standard or Proud, or b) sticking with the pre-equipped accessories in Beginner. In short, just to be safe, don't bother going to the equipment menu.