In formal, written English, whom is correct here:
I wanted you to listen to this interview by an author whom many of you already read.
In the answer you referred to (The easy way to tell which is technically correct is to substitute he and him for who and whom, then rearrange the word order to see which sounds right.), it looks like you skipped the part about rearranging. Substitute first, then rearrange:
who many of you already read --> he many of you already read --> many of you already read he
whom many of you already read --> him many of you already read --> many of you already read him
What's tricky in these constructions is that whom is an object but it comes before the subject.
Some have declared whom to be dead, but it isn't—not yet:
However, if you are writing at work, at college or university, or for
publication, it is acceptable and even advisable to use the more
formal whom, especially in constructions with a preposition.
Source: Lexico: "Who" Or
In spoken or informal English (as your example utterance is), the rule can be relaxed, and indeed, is better dismissed altogether if you want to sound normal.