On WBgames CBWardog said this regarding the overlapping skins problem:
"well, as i read the comments, i found out that many people had trouble using the origins batsuit mods, but had no problem with other skins mods. Also, when they used origins batsuit mods, they noticed some kind of "double skin", like the textures where mixed up. Well, it is actually a mod problem. As i thought, the mods where made in high resolution. I took for example, the CJs The Dark Knight Suit, and extracted its textures. there are no 1024x1024 textures, so i added them myself (using loggin mode to get the code of the textures, and then adding them in the .log file) and now it works! It was just that, the modders surely play with high resolution so, they extract just the hd textures
If anyone wants to fix it themselfs, you need to add 0x154F425F, 0x61A6E079, 0xE05BDED6 and 0xBB92A413 (those are just suit textures and the damage texture, no shaders or normal maps). So modders, please add those textures in future mods to help us."