Please take the following with the largest grain of salt that you can find, as I am not the expert in this department.
It's my understanding that the brachioradialis aids only in flexion, not extension.
There are two muscles, the extensor digitorum and the extensor carpi ulnaris, that aid in the extending of the elbow. The extension of the elbow by these two muscles appears only to come after extension of the fingers and/or the wrist. At best, I think these muscles are subordinate to the actions of the triceps brachii and the anconeus.
Discounting the roles of the triceps brachii and the anconeus in the extending of the elbow requires intoxication.
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