Don't be too discouraged by job postings requiring an EE or CE degree. At my last two companies (a network gear vendor and a hosted VoIP provider), our postings stated EE/CE was preferred for new grads, but what we really needed were folks with systems programming experience and an understanding of the SW/HW interface.
If you've internalized most of your systems classes (OS, computer architecture, compilers, networks, etc) and are comfortable mucking around in C/C++, you're no worse off applying for these jobs than most new EE/CE grads.
If you've internalized most of your systems classes (OS, computer architecture, compilers, networks, etc) and are comfortable mucking around in C/C++, you're no worse off applying for these jobs than most new EE/CE grads.