Well, unless one of the texture experts knows a really neat trick, I doubt this is possible for two reasons:
1. Accessing and altering files on the xbox is very difficult. The console has not been designed for that kind of accessibility (rather the opposite) and modding software on it most of the time also entails modding the hardware as well. Not advisable if you are not really very sure of what you are doing.
2. And this is the point that really breaks the back of this possibility: The xbox 360 has very limited memory (I think it's as little as 512 MB or something). Personally, I think it's a minor miracle that developers could make games that look this good on that kind of outdated hardware but one of the reasons they can is because they use every shred of resources the xbox has to offer. When they design a level, they have to weigh how many models, texture, animations and sound elements they can use before they fill up that limited memory. So, even if you could install 4k textures on your xbox, the hardware would not be able to load them.
So sorry to say, that ME3 is probably as visually impressive as it can be on the 360.