It would be nice to have a way to do a "make build" (or equivalent steps)
   without having to overwrite your existing "/usr/include" tree with a -current
   tree in order to build a -current kernel/userland.

You can already do that.

setenv DESTDIR /new
mkdir /new
cd /usr/src/etc
make distrib-dirs
cd /usr/src/include
make install
cd /usr/src/lib
make && make install
...

There are currently only two things that *have* to be updated in the
running system during a build:

* /usr/share/mk
* /usr/share/tmac

Everything else should use the files in $DESTDIR if it's set.

   In other words, the
   existing build is pretty much self-contained within the "/usr/src" tree (or
   wherever you're building from), it would be nice if it was totally
   self-contained.  Of course, I don't know how hard it would be to do this, since
   I'm sure the compiler might want to still search "/usr/include" even if you've
   somehow recursively fed it "-I/usr/src/include".

This isn't good enough.  Some of the include files are installed from
other places, like src/lib/libcurses and src/lib/librpcsvc.  These
need to be installed before you can build the rest of the system.