is there a trusted compilation service that uses a distributed agreement mechanism, à la blockchain or DHT for validating some git/svn hash against a binary.
every downloadable source publishes its own binary hashes but the whole practice is somewhat moot in the event of server compromise, not to mention build reproducability.
True, although if someone was going to put a backdoor into a compiler, they'd have to be idiots to attack tarsnap; much better to have it trojan an OS kernel or something else which is trusted and far more widely used.
You can compile the client code yourself. In fact, until recently you had to compile the client code yourself.