On the other end of the spectrum would be to summarize it in the shortest form with the simplest words, instead of with many and multi-syllable words. How about this (not mine, I’ve heard this in addiction recovery rooms, where apologies and amends are often discussed):
In the sentence “I’m sorry I did x, but you did y”, the word “but” means “disregard the above.”
But,
Whenever I catch myself reaching for “but” I recognize it is because I need to feel heard. What I did was unacceptable. But I didn’t do it in a vacuum and I need my grievances to be recognized. My belief is that omitting the “but” phrase is an act of faith. You need to trust that the other party cares about your feelings and side of the issue, too. Accepting an apology is just as delicate an act as giving one.
“I’m sorry I hit you with the blue shell.”
“I appreciate you saying that. I know you were in last place and that must have felt awful. I don’t want that for you either.”
I understand the urge to feel heard AND whenever we bring something that may contrast we risk the disagreement connotation that “but” carries to trigger the recipient’s defensive reaction (even if unconsciously)
They asked me if I thought it would be a fun team-building exercise to bring in their improv coach and do a class with a bunch of VPs and directors. I said no.
I understand the concept but sometimes people can be overzealous about their passions.
EDIT: I understand the concept and sometimes people can be overzealous about their passions.
“I felt X, Y, Z, so I did P, Q, R, but I’m sorry for that because it caused you A, B, C.”
Your usage of “but” still invalidates the preceding phrase on behalf of the latter, which works here because the affirmed phrase is the apology.
I don’t think there’s anything wrong with stating your side — but if you mean it, end on the apology.