Managing sub-projects

I'm trying to create a git repository for a tool chain for a proprietary processor. I'd like to create a private repo with documentation, build scripts, etc., which includes several sub-projects: binutils, gcc, newlib, etc. Each of the sub-projects will have a branch which has support for the new processor. These branches need to be maintained in my repo, not in the upstream repo. I want to be able to periodically rebase these branches from the upstream repo.

I've looked at several schemes, but each one seems to do something other than what I want.

Git submodule: Branches created in the sub-projects are pushed to the upstream repo, not to my repo. I tried to change origin and created an upstream reference, but was not able to get changes pushed to my repo.

git subtree:  Does not maintain sub-project history or allow rebase.

git slave: Requires multiple private repos. Appears to require the same branch names in each sub-project.

repo: Appears to work a bit like git submodules, where pushes on the sub-projects go to the upstream repo, not to the private repo.

Any other ways to do what I want without creating a separate forked repo for each of the sub-projects? Or have I misunderstood one of these schemes?