As far as I know, Ethnic Artstyles is on par with patch 3.13?
Some definitions apparently aren't.
CIV4ArtDefines_Unit.xml
Spoiler :
For the chariot, the correct shadow would be (pre 31.3 already)
<ShadowAttachNode>Chariot_Chariot</ShadowAttachNode>
interestingly, the shadow of the 'national' versions (e.g. chinese, european etc.) still use 'your' / the old shadow.
The chinese archer button was fixed in 3.13 (was longbowman before)
<Button>,Art/Interface/Buttons/Units/Archer.dds,Art/Interface/Buttons/Unit_Resource_Atlas.dds,4,1</Button>
The eurasians, european, greco-roman and south-american spearman button was changed in 3.13
<Button>,Art/Interface/Buttons/Units/Spearman.dds,Art/Interface/Buttons/Unit_Resource_Atlas.dds,4,6</Button>
interestingly the regular one was like that in 3.02 already (you still use the warlords one).
CIV4FormationInfos.xml
Spoiler :
Just one change, in the "BATTLE (1)" formation, the GENERAL entry was updated in 3.13.
I was too lazy to check all changes in CIV4UnitInfos.xml, but the first two did change form 3.0x to 3.13 (explorer and swordsman got <iConscription>1</iConscription> instead of 0). I assume the rest is also correct, so you can use the 3 files Roamty provided, he knows what he is talking about

Since you load in a modular way, I believe you would not need most of these definitions in the first place, so maybe you should experiment with removing them, then you wouldn't need to worry about them changing.
Chances are you actually inherited them from EDU, so you might want to look into the modular version of EDU I made a while ago as it inherits most of the changed definitions (it will need adjustment for the chariot shadows of the chariots included in EDU, all else is simply inherited - time to update it as I include it in my mod I guess).