I'm just a reviewer and can only comment on what I've experienced. But I can say that what you're asking has definitely been done.
Sounds like you need two or three people dedicated to the task. Documentation is a whole profession by itself. Well, good documentation.
Isn’t that potentially a huge problem? What if your reviewers work for my company’s competitors? I don’t want them seeing our code base. Do you have any methods to ensure that doesn’t happen?
IMO: Target shops where they just don't have the expertise on-hand to do thorough code reviews. Don't waste time trying to convince a team full of experts with deep domain knowledge that they need you. (They probably don't.)
We also have a "problem" where there are some components that are a different language than what most of us are experts in, so they end up being developed by a solo developer. When we need to jump in, as we learn the codebase, we also see novice mistakes that are very hard to fix, because we just don't have many years of experience in that language / platform.
Thus, IMO, on your website, list out situations where shops will clearly identify a need for your service. (Team full of novices, solo developers, team members quit.) Don't go trying to convince "everyone" that they need you.
One thing to note about our service is that we are not trying to replace your code review process if it is already working well and we strongly agree that knowledge transfer is a very important part of code review. ( We actually have code review metrics as well that help encourage and reward your internal code review process. ) However what we do believe and see on a daily basis is degree that we help supplement the process and help catch many issues as well as inject a unique perspective. Our reviewers are all highly qualified, many are maintainers of popular open source projects or work at top tech companies. Our reviewers also gain context over time similar to a new senior engineer on your team. Reviewers also can share notes with each other to build up a corpus of information for your project over time.