As far as I understand the attack, the attacker brute forces his own DH secret, not the DH parameters. So attacker has the parameters for both connections, gets

As far as I understand the attack, the attacker brute forces his own DH secret, not the DH parameters. So attacker has the parameters for both connections, gets the public keys from both chat partners and then brute forces two secrets such that the hashes of the resulting DH shared secret match. For this the attacker needs 'only' to brute force the keys, not the parameters.