I'm not sure your solution solves that. If Firefox has vulnerabilities in the source right now, you do little to protect yourself by compiling on your own. Even if you can verify that you and someone else produce the same binary, they could just both be vulnerable.
In fact, if you compile it yourself, unless you can verify the compile against a "known good" one, then you can't even be sure that your local toolchain hasn't been compromised. (I mean, sure, if you were a perfect auditor of your entire toolchain, then you could have some confidence here. You have to be perfect, though.)
Consider, you do a compile of Firefox and it is different than the one for download. Why? As things stand now, you don't know. And that is the problem.