Hmm, code signing might not help us due to some specifics of how we do deployments and builds, but thinking a little more about it - what could help in an even bigger way here is PGP signing at the commit level. Git supports this builtin and recently there have been a few pushes for it's support on services. Probably have to hack together a little custom verification script, but I know of no reason that wouldn't be viable.
This would basically resolve my biggest problems with it I suppose, if used fully and properly. Currently comitting with your SSH key basically resolves this issue in the same way, assuming our internal-restricted server isn't compromised of course.
I'd still be a little uncomfortable putting code on 3rd party servers and having any data there at all for stability reasons, but this does make it more viable. I'll definitely be commit signing everything I have on cloud services from now on.