Here's another way to show the absurdity of attempts to misinterpret the militia clause: that clause is followed by one that says this: "the right of the people to keep and bear Arms shall not be infringed." So if "well regulated" means controlled by government, or "militia" means a government force, the second clause becomes a non sequitur (meaning does not follow logically). So here's what those liars are claiming that the 2nd Amendment actually says: Arms shall be controlled by government, therefore arms shall not be controlled by government. A, therefore not A, in other words. The argument is absurd.
To build more directly on the OP, comparing the 2nd Amendment to the 1st in gun control debates can be a good way to shed light on the lies of gun control, and if anti-gun bigots claim that it's an apples-and-oranges comparison and therefore not relevant you can point out that there is much truth in the saying that the pen is mightier than the sword, and it can be as destructive. Just look at how liberals always complain about money corrupting the elections that determine who leads our nation. And what does that money buy? Access to the proverbial pen, using the 1st Amendment right to wield it. Our 1st Amendment rights, in other words, are what determine who runs the country, much more so than our 2nd Amendment rights (thank God), so they do allow the exercise of a great deal of power, and that power can be very destructive.
One place this comparison is useful is in the argument that when the 2nd Amendment was written the modern arms of the day were single shot and slow to reload. There are other flaws in that argument, but one is that the same thing could just as easily be applied to the 1st Amendment, since when it was written the press was literally the press. Just as 20th Century arms (so-called assault weapons by the liars who try to outlaw them) are more powerful than 18th Century ones, 20th Century information media are more powerful too. So a law against 20th Century arms is like a law giving government exclusive control over 20th Century media, meaning television, radio, the internet; all electronic media in other words. Those who try to destroy the 2nd Amendment sow the seeds of the destruction of the 1st, and if the one goes the other will follow.
Or apply the comparison to gun buy backs. How about a government-sponsored book buy back, where copies of the Constitution, the Bible, and other politically incorrect books can be turned in with no questions asked.
No argument will have any effect on the hard core anti-gun bigot, because he is not interested in truth or logic; he is ruled purely by hatred and intolerance. But many who support gun control do so out of ignorance, and this kind of argument can affect those.