The more I think about it, the more I think that bootstrapping the build isn't actually the huge problem it first seemed to be. There are practical problems to solve, but they CAN be solved.
In contrast, how can you make sure that the actual payload code hasn't been tampered with? It is written in a high-level language, but it gets stored and viewed on devices that have backdoors in their CPU microcode and huge OSes that can hide god knows what. The author can sign the code, but that doesn't tell anything other than it was really the author who signed it and the code hasn't been modified afterwards -- if the author's system was compromised, the code can contain backdoors before being signed. So you need to validate the (signed or not) code to be correct, but you're doing so on an untrusted system. It goes on and on.
You'd probably need the code to be verified, then signed, by a trusted party on a trusted system. THAT signature then means the payload hasn't been tampered with, and can be trusted after it gets built on your trusted system (and this is where the bootstrap problem happens, and gets solved).
All this is obviously still glossing over the problem how to obtain hardware you can trust.
...edit: But if you have all that, then you don't need a complex bootstrapping anymore. A trusted actor can verify, or even build, a trusted system by hand on trusted hardware, sign it, and then you can use that (binary!) as long as you run it on your own trusted hardware and verify the signature first.
The bootstrapping then becomes a tool to ensure reproducibility, but is no longer needed for trust.