"And if that replacement was Joe Biden....?" I don't think that would work.
I googled this: The vice president is an elected official, and is not part of any executive branch chain of command.
Still working on in what cases the VP could assume the office of president...
Amendment XX Section 3. If, at the time fixed for the beginning of the term of the President, the President elect shall have died, the Vice President elect shall become President. If a President shall not have been chosen before the time fixed for the beginning of his term, or if the President elect shall have failed to qualify, then the Vice President elect shall act as President until a President shall have qualified; and the Congress may by law provide for the case wherein neither a President elect nor a Vice President elect shall have qualified, declaring who shall then act as President, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a President or Vice President shall have qualified.
Looks like we're screwed either way...