This is a hard one for me. Like you, I recognize that all people and cultures embrace the concepts of self-reflection and apology. But also like you, I feel a little squeamish about the conscious appropriation of rituals. Mine or anyone else’s.
When I was a kid, I sometimes attended mass with my mom (who isn’t Jewish). Even then, at a young age, I felt like there were lines that I shouldn’t cross. I would sit and sing as to not be a distraction, but when it came to saying the creed or taking communion abstained. To participate in a ritual I didn’t fully understand or believe felt disrespectful to those who meant it.
Now as then, I sense a lack. I don’t feel entirely comfortable answering this question, because I’m unable to provide you with a halachic answer. But I can commiserate with your feelings, and say that if I found myself in this situation, I might be inclined to voice my honest emotional response, as an individual.
I might want to say this: “Teshuvah isn’t a discreet experience. It’s part of a much bigger cycle. To lift it out from the rest of the year, divorced from a larger Jewish experience, feels incomplete to me.”
But here’s the catch: though I’d want to say those things, in the end I’d probably keep silent. It’s not really your job to police what your friend chooses to do, and my instinct is that anything you say along these lines will fall on deaf ears. Faith and practice are so very personal, and you’re likely to create some tension if you try to tell him what to do.