Is it "Whoever she married would know the truth" or "Whomever she married would know the truth"?
My feeling is that the latter is correct ("whomever" being the object of "married" and "whomever she married" being the subject of "know"). I hesitate because while I have seen clear explanations as to how an entire clause containing a "whoever" or "who" can be the object of a preposition (eg. "give it to whoever needs it the most" and "depending on who is offereing it"), I haven't seen anything that states clearly that a clause containing a "whom" or "whomever" can be the subject of a verb. Would I be correct in saying that if I can replace by"the person who", it's "whoever" and if I can replace by "the person whom" it's "whomever"?
A. You're absolutely right. "Whomever she married would know the truth" is the correct form because, as you point out, "whomever" is the object of "married."
You're also right in assuming that if you can replace by "the person who," it's "whoever," etc.
The clauses in your examples are noun clauses. A noun clause can do just about anything that a noun can do. It can be a subject, a direct object, or an object of a preposition. Whether to use "who" or "whom" in a noun clause depends on what it does in the clause, not on what the clause does in the sentence.