Re-building Linux kernel without "clean"

The make clean is only for the deb-pkg target. Take a look at scripts/package/Makefile:

deb-pkg: FORCE
        $(MAKE) clean
        $(call cmd,src_tar,$(KDEB_SOURCENAME))
        $(MAKE) KBUILD_SRC=
        +$(call cmd,builddeb)

bindeb-pkg: FORCE
        $(MAKE) KBUILD_SRC=
        +$(call cmd,builddeb)

If you build the bindeb-pkg instead, it won't do a clean. You probably don't need the source packages anyway.

I suspect it does a clean because it doesn't want to tar up build artifacts in the source tarball.

You could try producing those deb packages with a different tool, make-kpkg that is installed by apt-get install kernel-package. Then for example

make-kpkg --rootcmd=fakeroot --initrd --uc --us -j2 kernel_image kernel_headers

This command should not do a make clean each time.