There are others who have posted their experience, generally, it's not advised to do. Me, I never ran across the OM (yet). But from what I know, odds are it doesn't do much good, but can do quite a bit of harm.
I have considered writing a friendly letter to my wife's "boyfriend" to share with him my desire to reconcile with my wife... if I were in his shoes (which is hard to imagine), if my lover's husband were really sincere in his desire to reconcile with his wife and own up to his role in his marriage's disintegration, I would want to know that. I would probably discuss it with her and encouraged her to consider giving reconciliation a chance. This, of course, assumes he has a functioning conscience
It also assumes living in a prefect world. But then again, in a prefect world, you wouldn't be in this sitch. In the real world we live in, any reasoning with the WA is pretty much ignored by the WA, whether it comes from you, friends, relatives, workmates or the OP. Why? Because the WA is acting according to their feelings, not reason. And their feeling is that "ILYBINILWY", and that will simply rule.
When my wife left me, she accused me of being controlling and emotionally abusive. I wasn't convinced the shoe entirely fit, but if it fit at all, I had no desire for it to. So I got myself into individual counseling as well as group counseling related to abuse. I've been taking my wife's stated concerns seriously.
Good for you.
But she says she doesn't really care, which I now suspect has a lot to do with her involvement with the OM.
To some extent, yes, attention from another is distracting and filling her emotional void right now, it has her [falsely] feeling that she's "moved on" and it's also that she's further along the "emotionally detached" path than you are; she's had time prior to the A where she was withdrawing from your relationship.
I just feel like, since I vowed to allow nothing but death separate my wife and me, would it not be good and right for me to take a stand for our marriage
This is a common feeling, to hold to the vows. My belief is that's your right to do so, and trying to "save the marriage" is a noble thing to do if the intent is right, yet I think it clouds reasoning some when figuring out how to go about this (as, for example, it can feed into one's sense of "righteous indignation" which can then hit you in the face if you act on it). To me, it's not a matter of holding to vows for a marriage where one partner has already broken those vows, because marriage is a contract, and that contract's been breached, thus releasing the other partner from it. The bottom line is not so much the keeping of vows anyway, but of wishing to repair the broken relationship. That may require a course that takes you through the vows, into divorce, out of the vows, through some streets of Hell, through the thick of the forest... who knows?
I want him to get the impression that I'm not a jerk
What would make you think he's labeling you as such, and why does it really matter if he does or not? There's no difference if an OP considers the LBS as a "jerk" or as "a nice guy but not the right guy for this gal", really. That statement of yours suggests more that it arises from your perception of yourself at this moment, not wishing to be seen by the "competition" as a "fool", dealing with the rejection you feel, or something along those lines. If you look deep inside you, this may ring true.
It's all in the way one looks at things. take your focus off the OM, and these feelings disappear. You're not a "jerk"... Jerkish behavior does not encompass trying to repair a relationship, but quite the opposite, wouldn't you agree? The OM may even generally be a "nice guy" but doing an unethical thing, taking the low road, which makes him beneath you. Therefore, if anyone's displaying 'jerk behavior', it's the OM... so why bother being concerned at all with what this stranger, this man who is beneath you, may think of you?
I had one female friend of ours, when I ran this idea past her, say that she thought fighting for my marriage in such a way might possibly make a good impression on my wife.
Women love, love, love that "White Knight" type of stuff in their romantic fantasies. You see it a lot in Harlequin novels and movies, it sells!... and it influences their real life so that they'd like it there too. But in real life, it works differently, you don't ride off into the sunset happy ever after. That's because "taking a stand" doesn't change how the WA feels or wishes to do, nor does it change their perception of the primary relationship nor does it repair it... in real life, it may impress them favorably, or it may repel them.
In my sitch, early on a couple of days after the bomb, I did that. Went to go get my wife and physically bring her back home, dammit! Climbed the Ivory Tower, but she wasn't there. Feedback was she was impressed, liked it much, but...
Maybe what it demonstrates to them is that they're desired, strokes them some. I'd say though, that at best, "fighting for the marriage" in such a manner doesn't do anything today, but can be a pleasant memory for them that maybe becomes a teeny morsel later on when and if your sitch becomes more viable. But all the same, I'd think that fighting for your marriage in a more DB sort of way creates favorable impressions too that are probably, on a longer term basis, more constructive.