Is Being Right a Sufficient Tactic Against Heresy?

First off, I am sicker than I ever remember being, so if the following makes little sense or sounds half-baked, just back off and cut me some slack or I’ll cough the bubonic plague on you.

My Catholic readers make a big fuss over the fact that, according to them, there is no "principled difference" between Protestant theology and heresy. What they mean is that when a Protestant debates a Mormon, the conversation may go something like this:

Protestant: "You’re wrong about Jesus, you know. He was God."
Mormon: "Nuh-uh."
Protestant: "Yeah-huh!"
Mormon: "Prove that I’m wrong."
Protestant: "OK, look at these verses."
Mormon: "Fine, but first I want you to look at these verses."
Protestant: "Nice ten-speed" (slams door).

The Catholic (claims the Catholic) is not doomed to forever spin in a circular prooftext battle, for he alone can appeal to the historic succession of bishops stretching back to the apostles. His position, in other words, rests both on appeal to Scripture but also upon a version of apostolicity that is actually verifiable rather than invisible.

So here's my question: How does Paul the apostle tell his readers to deal with heresy that would eventually arise?

Let's consider a couple texts. In Acts 20, Paul bids farewell to the Ephesians, telling them that savage wolves would invade the flock from within and without. He then says, "Therefore I commend you to God and to the Word of his grace."

To his protégé, Timothy, Paul says that his heretical opponents must be dealt with gently and peaceably, without quarrelsomeness, if perhaps God might grant them repentance and the ability to know the truth and be spared the devil's snare.

In both cases, doctrinal error is to be combated with doctrinal truth, and in neither case is there any sentiment that says, "Riiight.... Can we have a look-see at your list of bishops? Oooh, don’t got one, do ya? Thanks for playing, the consolation prize is available in the losers' lounge."

I’m not denying the role that such succession may have played in the early church, but I am wondering if something that began as an circumstance of history has become a litmus test that excludes others who may actually be right.

I mean, once the locus of our worship ascended to heaven, the significance of historical succession seems to have ceased. Jesus is not a priest after the order of Aaron, but it doesn't matter. Gentiles can't trace their heritage back to Abraham, but so what, they were spiritual Israelites. So why can't apostolicity be spiritual as well, rooted in truth rather than genealogy?