A one level dip in Fighter, and using an item called the Sash of the War Champion. It increases your effective fighter level by 4 for Bravery and Armor Training. Level 5 fighters can move full speed in Medium armor, as well as reducing the ACP and increasing Max Dex.
Or wear Mithral armor of some kind, if you like simplicity.
If you are especially wealthy, you could combine the two ideas, get some Mithral Full Plate. Mithral Full Plate would be considered Medium Armor, you would move full speed, as well as keep your Barbarian Fast Movement.
A third option, be a dwarf. If you aren't a dwarf, kill yourself and have your friends take you to a Druid ( at least level 7 I think) and have them cast Reincarnate on you until come back as a dwarf. This could get expensive, since your new race is random, but you could get lucky.
I don't recommend option 3, it just seems silly.
at what point does ACP affect move movement speed.
Never. It has to do with the type of armor you wear. If you wear mithral its treated as light armor for the purposes of movement, so your barbarian would have a base speed of 30 in the armor, +10 for the fast movement. If you hit 0 ACP you can wear the armor without incurring an armor check penalty(which only applies to certain rolls), but it doesn't affect movement in armor.
Edit: to clarify, medium/heavy armor reduces your movement speed, ACP has nothing to do with it.