Understandable, and I think Adywan is on the same page as you for ANH:R:HD. I might just do my own version of the audio track with the March inserted for myself.
It’s not that I don’t think it fits - the imperial march fits perfectly imo for the Death Star reveal - but it takes away from the first time we hear it in ESB.
Regarding Battle of the Heroes, I don’t really think it fits at all.
I actually agree with both of these, but in the context of the entire saga (yes, even the prequels…) it’s odd that the March is completely absent from Episode IV.