I take back what I said about the kernel not mattering. You may be right, some of the compiled tools do not support an older kernel version. However, I don't think we need to recompile the kernel, just the non-working tools. It's most likely a low-level lib. I'm guessing glibc & friends because it went from 2.5 -> 2.12 on the Kindle 4.
EDIT: I'm curious why Amazon included glibc in their sources for all versions up until 4.0 Did they forget? Anyways, it seems like Amazon never edits glibc, so we can compile the vanilla sources:
http://ftp.gnu.org/gnu/glibc/glibc-2.12.1.tar.bz2
Cross compile that for arm targeted at a lower kernel version, and we might get a working bootup.