You are getting to the gist of why RM (the 'Big Daddy' of HARP) has it's combat rounds broken up into segments: Snap, Normal, & Deliberate. And it is why I go for more flowing combat styles, not the: on my initiative I do items 1 thru 14, style.
It is very easy to institute initiative mods for actions, or just do it on the fly. Say you have 2 fighters (A and B) and they are 18 feet apart. Fighter A gets a 17 iniative, while Fighter B gets only a 6. Fighter A says he will rush and attack, which means he has to move about 15 feet (assuming he is using a broad/long sword) You say that moving that distance makes his attack go later, say with a -10. Well, luckily for him he was 11 over in initiative verses Fighter B so he still attacks first.
Of course, you could easily say that the distance has to be covered no matter what for the 2 fighters, so the initiative is there saying: "when they get close, the one with the higher initiative goes first." In this case, the movement modifier to initiative would only apply to someone not directly involved in the attack/defend between Fighters A and B. (Say, an archer wants to help his buddy Fighter B by shooting Fighter A before B gets attacked by A.
I suggest is that you imagine the fight in your head and "watch" it as it unfolds, and then go with what feels/seems right to you.