32-bit Python + 32-bit CXfreeze is supposed to produce a working .exe, but for whatever reason the .dll it generates doesn't work.Try a different build tool than CXFreeze. Google "how to build 32-bit embedded python for windows" and similar strings. The final solution upon which you come should be relatively trivial to execute. It's just a matter of compiling for 32-bit and linking against a proper 32-bit embedded Python library. Consider this a learning experience.
It should be relatively simple for a developer, hence making it out to be simple. I say 'relatively' in reference to how important it is if you're going to hinge the success of all these mods on it.
CXFreeze should just be a wrapper around a compiler / proper build process. If it is so limited as to only support x86-64 binaries (which is the absolute opposite of how things normally are-- over 80% of the programs installed on my system are 32-bit simply because they're only available in 32-bit), then you need to upgrade build tools. Don't just give up.
I would offer to help directly, despite not knowing any Python specifically, but a) I suspect that you don't want direct, do-it-for-you style help with this, and b) I have other unaddressed reservations about the installer that severely reduce my motivation to invest time into it.
We're still looking into alternative solutions though.