"Alice, a system administrator who contributes to a Linux distribution, is building her binaries on servers that, unknown to her, have been compromised"
This is a bit of weird scenario.. so they're assuming the only build being compromised is the one that ends up in the repo and no one can confirm that easily. So just have two (or more) identical servers in separate locations under different people's control so they aren't both compromised? No need to fuzz the dates and paths and stuff. Or if you really want, you make a special Debian version (super-stable) with fixed clocks, file paths, etc. where things are easy to reproduce.
"Bob, a privacy-oriented developer, makes a privacy-preserving browser, but is being blackmailed into secretly including vulnerabilities in the binaries he provides. Carol is a free-software user whose laptop is being attacked by an evil maid called Eve, the third developer of the title; each time Carol shares free software with her friends, it is pre-compromised by Eve"
Do Debian contributors just upload a binary blob to the Debian servers and that's it? I though they were saying they have build servers for every package and the source from which it's built is available
How about even easier - a bribed/black-mailed Debian maintainer slips in a patch to some of the tens of thousands of packages they tweak, no one notices and it gets distributed to everyone. I'm not expert, but it seems the smarter solution would be to have a much smaller reproducible core/base system (with Debian patches when necessary). Something that can realistically get enough eyeballs on it. And then everything else is built by project maintainers into something like flatpaks/snaps with no patching.