Cross-Architecture Package Sharing?

I am not quite sure I have understood your question. However I believe I updated https://trisquel.info/en/wiki/cloning-system-or-how-make-copy-installed-packages-one-computer-another to answer it! :-)

Basically, you have to download again the DEB packages that are architecture-dependent but you can still copy the remaining ones (/var/cache/apt/archives/*_all.deb) from one system to the other and save a little bandwidth.

https://trisquel.info/en/wiki/cloning-system-or-how-make-copy-installed-packages-one-computer-another gives different ways to manually transfer the files. However, since we are talking about updates, 'rsync' would be appropriate. To only fetch the /var/cache/apt/archives/*_all.deb files that are different. And you can define an 'alias' (e.g., in ~/.bash_aliases, assuming you use Trisquel's default shell to update your system and ~/.bashrc executes ~/.bash_aliases, as it does by default) that would fetch the newest /var/cache/apt/archives/*_all.deb files from the other computer and then launch the update.

Thank you, Magic Banana!

Your answer is extremely helpful. It isn't a complete answer, but (as you note), the question itself was extremely confusing.

I think- though have yet to completely verify- that I've worked out a way to implement what I needed. I may put it on the wiki if it seems reasonably general.

Once again, thank you!