What happens if I'm a new node that just finished syncing, and receive a 20-min block with reduced difficulty? I have no way to know an agreement has happened, and will reject the block.
So? You'd be one node of the thousands... you're rejection should have no bearing on what the other nodes do...
That means that if your proposal was accepted right now, there would only ever be 7118 nodes for ever and ever. No new node will be able to join because they see an invalid blockchain.
once the other nodes confirm the block and a subsequent one, would your node not then accept it as being part of the chain and move on? Seems highly illogical and a major flaw in the design if it wouldn't.
Highly illogical? It's the other way round. A node shouldn't care what the other nodes do, it should be able to validate the blockchain on its own. If not, then we start to add trust to the system, which is precisely what Bitcoin is designed not to need.