Your point about partial ordering is very powerfully appealing.

However, I feel that any increase in utility from mere accumulation tends strongly to be completely overridden by increase in utility from increasing the quality of the best thing you have, such as by synthesizing a symphony and a theorem together into some deeper, polymathic insight. There might be edge cases where a large increase in quantity outweighs a small increase in quantity, but I haven't thought of any yet.

(Incidentally, I just noticed that I've been using terms incorrectly and I'm actually a consequentialist rather than a utilitarian. What should I be saying instead of "utility" to mean that-thing-I-want-to-maximize?)