Does this exist: flatpak-like sand-boxing with gentoo-like source-based package management?
I assume it doesn't, but thought I'd ask.
I really like the principles behind both gentoo and flatpak, but right now I can only do the gentoo way or the flatpak way (and I've opted for gentoo's for now).
What I'd love to have from flatpak:
container like sandboxing and isolation
customizable sandboxing and permissions
What I'd love to have from gentoo:
powerful build system building packages from source
global declarative management of compilation options
Does Guix fit your criteria, perhaps? If you haven't heard of it, you can think of it as Nix with a Lisp frontend.
I unfortunately am not very experienced with containerizing packages so I can't say much, but I know you can do it; the Nonguix channel employs containers for some proprietary software.
Like Nix, Guix has all that building-from-source stuff you'd want from Gentoo. There's recently been work on making parameterized packages (the Guix equivalent of USE flags) a thing, but it's still work-in-progress.
Ignoring the steep upfront cost of learning it, I'd say Guix makes it incredibly easy to add your own packages. Here's the custom packages I currently have in my dotfiles repository. I can import one to my main config file, add the package, and it gets included in my environment the next time I reconfigure it.
As for patches, I can't make any comparisons since I'm not familiar with Gentoo, so I think a code snippet is probably better for you to judge if you'd like it.
Not sure if this addresses your concern about multi-architecture support, but the Foreign Architectures section of the manual discusses what you can build to.
EDIT: So I was curious after posting this because usually the CLI often has much less verbose options (like --with-input for replacing inputs), and I started wondering if there was any procedure that would make this simpler. Turns out there is :) I've included it under the example. Although, I suppose I should have mentioned you could write your own if you really wanted to.