The solution for the "singleton problem" is to put the implementation code into a separate part of the header behind an #ifdef XXX_IMPL, and only define this before including the header in one place in the project.

This is also the approach used by this library, see:

https://github.com/jeremycw/httpserver.h#example

This approach also doesn't have the 'build time problems', since the (expensive to compile) implementation code is only seen once by the compiler (unlike many C++ header-only libs, which rely on inline code)