OK so I'm a liar. I had other things on my plate. I might still get to it, but it'd be better not to depend on me. It is a pretty straightforward compile, however, so if you're motivated you can do it yourself. Of course, it's Emacs, so it won't be particularly small. And in my brief experiment, compiling without the GUI didn't trim much fat at all, so I'm not even going to bother. And I certainly won't bother going through the source tree carefully to trim off 'less used' features. It's too hard to decide what those might be both for me and for you, so, with the exception of the 'obsolete' source dir, I'll just leave the whole thing in. Emacs would be well served by a general 'extension remastering' script, which each user can use to easily trim what is fat *for them* and rezip back into a .tce. It looks like there are a lot of less-used features which would fail reasonably gracefully if you just removed their .el and .elc files from the final product. But since this won't be a high-demand extension, it just makes most sense for users to do that themselves.
Still, even though Emacs laps TinyCore itself several times in size, TC+Emacs does leave you with a fairly capable (and these days you can even say 'lightweight') working environment.