So I'm interested in three things: Do other LWers recognize this pattern now that I have mentioned it? What decision did those that were already aware of it make, in order to optimise this activity?

...and a fanatical devotion to the Pope?

Yes, I'm aware of this and some related patterns.

A few things I have taught myself over the years (not exclusively related to this pattern) that have reduced the degree to which I feel bad in arguments, both online and off:

• I focus on understanding rather than agreement.
  That is, if I'm in an exchange with someone and I'm not sure that we understand each other's positions, we are not yet ready to argue. If they try to discuss how they're right and I'm wrong and why, my usual response is "Well, slow down. You may be right. Hell, we might even agree. Right now I'm not even sure I understand what you're saying and how it differs from what I'm saying."
  Some people get irritated by this and try to wave it away as pettifoggery, insisting that we get down to the important thing which is explaining why they are right.
  I disengage as quickly as practical from these people.

• I seek first to understand, then to be understood.
  That is, if I'm in an exchange with someone and we don't yet understand one another and we're both attempting to, my primary goal is to understand them. Usually, I find that their primary goal is to be understood, so right away we're cooperating.
  Often, I find that they have no real interest in understanding me, so I leave it at that... once I'm pretty confident that I understand their position, I articulate as clearly as I can my points of (dis)agreement with it and my reasons for same, and we're done. Sometimes I conclude that they aren't even interested in whether I agree or not, so I thank them for their time and we're done.
  Sometimes, they do seem interested in understanding me, in which case I will try to return the favor, explaining my position to them until they are confident that they understand it and can articulate their points of (dis)agreement with it and reasons for them.

• I attend to reasons for belief.
  For example, if I am defending a belief in X, and in that context I find myself arguing that Y, then I ought to consider Y, if established, a legitimate reason to believe X. If I don't, it's likely that I've switched to trying to win, and I should self-correct.

• I visibly attend to points of agreement as well as disagreement.
  If someone says "A, and B, and C, and therefore D, which because of E, gives us F" and I reply "No" I have implicitly framed our exchange as about whether or not F is true. If I reply "I agree about A, B, and C. I'm not sure D follows, though it might, and in any case D seems plausible. I don't agree about E, for this reason, and I see no reason to believe F" I have implicitly framed our exchange as quite a bit broader. Also, I've established a pattern of agreement as well as disagreement, rather than nothing but disagreement.

• I try to disengage without challenge.
  I find I'm often tempted, when I've decided to disengage from an exchange for whatever reason, to take a parting shot.
  I rarely find this valuable.
  I'm working on eliminating this tendency.

• I default to the first person. I find most exchanges go more smoothly when I talk about myself unless I have a specific reason to talk about the other person, or "most people", or "many people", or etc.