I wouldn't do such bill payments. Why do you want such attention? Make $1K-$2K payments at the time/visit.
If the only reason you're breaking up a large payment is to avoid 'attention', then you are structuring by definition. Bad news.
Now, if you're breaking things up because you're paying different cards, or because you're paying with GCs and can therefore only do $2k at a time, then that's different.
But if you want to pay a large amount to a single card, do it all at once if you can. Advising otherwise is not wise.