I worked on one once. It's harder than it looks. The coupling is so poor you have to jump through some serious hoops to get any usable power. Notice how the coils are carefully and neatly wound, and bonded.
Bigger coils would help, but these are already fairly good sized for some flashlights. What else would help is if you could get he proper magnetic core halves to make it a gapped core rather than full air core.
If I were interested in toying around, I would buy these and use a DC/DC convertor to get the output I wanted. It would be a much easier job than a scratch build.