Is there a Homebrew-equivalent for limited access user accounts in Linux?

Do you know pkgsrc? It's a framework (using Makefiles and some pkg_* tools) for compiling packages that also facilitates non-root building of packages (and their dependencies) very much.

So, referring to your choices, it's the "homebrew" thing but already built and proven, with lots of packages. There's a guide, too. (While it looks kinda NetBSD-specific, it's not and should work just as well on Linux.)

Linuxbrew is exactly a Homebrew equivalent for Linux. It may not have existed when the OP asked the question, but it does now and it works very well.