Ask HN: Proper way to fork a Linux distro?

Ubuntu makes a "mini" distro that is very stripped down. I'm using it and happy. Now I want to run this on other hardware but they do not provide a version for the architecture I want. https://help.ubuntu.com/community/Installation/MinimalCD

My question is how do I get to a place where I have the sources/packages of this distro that I can compile for the architecture I want?

There are so many distros in the world now that fork other distros (Kubuntu, LUbuntu, Mate) but it is surprisingly hard to get started doing it yourself. I am reading the LFS/BLFS docs, but this would take months to get started I think.

Edit: typo