I think it is an excellent idea to prepare this ahead of time. I suspect an effective apology is going to feature a number of different components.
Having said that, I think it is worth taking a cue from Prehil, who knows Lord Curo. Prehil seemed convinced that the "newfound land had addled my brains" line was insufficient, to the point of chasing Curo down and placing greater emphasis on the factor of Baris having been quite drunk. Prehil seemed to think that it helped to do that, and that Curo was a bit less angry after he did that. Of course, Prehil might be giving himself too much credit, but the fact remains that we don't know Curo, so we have no alternative insight about what might smooth things over with the guy. I would put more emphasis on the drink, where you are putting too much emphasis on your thoughts.
In other words, to my mind, the problem with your first draft is that it emphasizes too much the idea that you came to the conclusion that Neph was a fat coward by the cold application of logic to faulty facts. I think that does little to assauge offended honor, which is the crux of the problem. I mean, your explanation is basically "garbage in, garbage out". I think the mind of a medieval nobleman would be minimally swayed by that logic.
I think any effective apology has to balm the offended honor by assuring Curo that you hold his father in esteem, and that the words you spoke were the drink speaking, not you. You might, for instance, reference the dinner Neph hosted which you attended (session 50), your only in-person meeting of the man, and how conscious you are of the honor shown you in his Lordship's invitation.
Curo himself told Prehil what the apology should include, and I wouldn't suggest omitting anything. I believe a pledge to never again speak anything ill of the father in public or private was mentioned. You might even consider demonstrating your sincere contrition by pledging some deed by Sir Baris on behalf of the Curo family, to be named by Curo, in recognition of the sober way the guy has handled this (which you mention in your draft). Seems like something more concrete and honor-related, such as this kind of pledge, is more soothing to the medieval mindset, no?
Also, it should go without saying, part of the apology should include a disclaimer that your beastly outburst in no way reflected the views of your liege, that
parfit, gentil knyght.