Comma before "and that" in a compound object

The advice of the late Professor Trask http://www.sussex.ac.uk/informatics/punctuation/comma/joining is:

Use a joining comma to join two complete sentences with one of the words and, or, but, yet or while.

Your example contains two complete sentences. One is 'You should have known that he is quite adept at what he does' and the other is '(You should have known that) he has the best conversion rate'. So use a comma before and to signal the start of a new clause. The purpose of punctuation is to help the reader understand the grammatical structure of a sentence, and a thoughtfully placed comma will do just that.

Old thread but another one of my English grammar arch-enemies where I oscillated between the two outlined opinions. I finally came to rest at this:

14. Don't put a comma between the two nouns, noun phrases, or noun clauses in a compound subject or compound object.

INCORRECT (compound subject): The music teacher from your high school, and the football coach from mine are married.

INCORRECT (compound object): Jeff told me that the job was still available, and that the manager wanted to interview me.

Sounds reasonable to me what Purdue Online Writing Lab says, and this is what I do as a general rule. As pointed out in the comments, there are cases, where it is acceptable or even favorable to insert a comma, so this absolute statement "Incorrect" is ... incorrect.