6.01 in a Marui M4 S System?

[Muscleflex]

Hi all,
I have the above rifle I've had for 10 years now. I recently had the spring upgraded and it now shoots around 340fps.
I would like to make it accurate so would like to get an upgraded inner barrel for it.
Thinking of a 6.01... is this practical? (I'm willing to use good quality BBs obviously)
Also I don't know the length. I googled and first result came up as 370 for a PDI upgrade from ehobby asia http://shop.ehobbyasia.com/pdi-6-01m...l#.VwOg7vkrLcs

So is that the correct length? Unfortunately I tried to open my rifle up, I took the two pins.. but I couldn't pull the top receiver off. There is resistance and I don't want to keep tugging at it in case I break something.

If 6.01 is not practical - what's the next best thing? 6.03? I've seen a lot of topics on 6.04 on an M4 but why? why 6.04 and not 6.03 or 6.01?
Thanks