They won't try to stop you. The average persons indifference will do it for them. Most people won't build Signal from source or let you install it for them. Anyone who does won't get any updates, so over time the installed base would be vulnerable to attack anyway. Since less people would have Signal then less conversations would be protected by it in practice.

Why would they try to stop you, when they could just order Apple or Google to push out a backdoored update to the OS?

I wouldn't overthink it; the same way they "stop you" from dodging taxes, using illegal drugs, etc: the threat of violence if you're caught. https://xkcd.com/538/

The real question in my mind is whether they'd manage to overturn, or carve out an exception to, the "code == speech" ruling. [1] Would we actually see academics arrested for teaching someone how to craft an unbreakable encrypted message, let alone posting their code to GitHub? It would probably take a panic event far beyond 9/11 for the public to acquiesce to such a thing.

In practice, I suspect law enforcement just wants numbers, to nail more pelts to the wall, and would be entirely okay with choking off encryption at the source for average consumers: by outlawing the creation of mass-market encryption apps without backdoors. It's also not infeasible that they might try some sort of mandatory key disclosure, again enforced by threat of violence: "I, Alice, sent an encrypted letter to Bob on Feb 26th 2020, using key 0x123..., which I am hereby committing to the government database as required by law. I'd prefer you didn't use that key without a warrant, pretty please with sugar on top."

[0] https://www.eff.org/deeplinks/2015/04/remembering-case-estab...