Let's start with the fact that hydrogen peroxide self-decomposes over time during storage, naturally, the higher the temperature, the faster the decomposition, as well as local overheating when adding peroxide, where the temperature is much higher than the temperature of the reaction mass itself. Do not trust me, you can attach an empty bag to a reflux condenser and see how much oxygen is released from the decomposition of peroxide.
All conditions for polyhalogenation creates an excess of acid and the need to use peroxide in excess. I gave up peroxide a long time ago, it is the worst oxidizing agent for this reaction.