This sounds like a product idea to me. Make a website that shows the status of your friends that are willing to switch to signal. You send an invite to all your friends first so the list keeps up to date as soon as one of your friend made a decision. If everybody agreed you can switch as a whole. Even better if signal would implement it themself!

As far as I can tell, Signal automatically tells me which of my contacts are already on the app. If someone is willing to switch, the obvious thing to do is install it.

Well, your plan could work if all your future friends also agree to this.