Part of why the ImagePrint system lacks "strong" blacks is that their ICC profiles are actually a proprietary way of making more "linear" profiles (meaning more open shadows). If you don't have points in your blacks are that near 100% black then you will see your shadows go lighter than with normal ICCs. The best way to get good blacks with ImagePrint profiles (other than with a stronger K ink to start) is to also make sure you soft-proof with those profiles and then manually tune your blacks a but darker.
I bet you that it's not the ICC that is mapping the K to the LLK. I bet it's in the ImagePrint rip itself that the re-mapping is happening. In that case, you would be able to build your own ICC if needed. Most likely you won't need a different ICC though.