My fastest is 4:33 - I dunno if I'll be able to beat it with Melee. I think you have to use drygores on p4 to get faster (it's what most pro melee users do).
From what I gathered (obviously didn't do much testing with kill speeds using melee), it seems that the benefit from Melee is mainly less food consumption. Kill speeds didn't really seem like a massive improvement (2/3 path 2). Maybe Melee helps more with minion rotations? Not sure.
Using Range on 1/3 path 3 is kind of slow. I get like 7:30-8:30 kill speeds. I'm not sure what the optimal kill speed for this rotation is
.