Post-quantum hybrid encryption
Does using a slow-hash on the output of an asymmetric key-exchange
  
  offer any more protection in a quantum-computing era?


No. $\:$ A quantum attacker would simply find seed even if you didn't use "a slow-hash on" it.



  Is the algorithm (greatly) diminished, or completely broken?


The algorithm will still be completely broken by quantum attacks. $\:$ Furthermore, your simplified

protocol would just have one more link (scrypt) that could potentially be broken by classical attacks.