Each tefilla of Yom Kippur has a pretty clear theme, except for mincha. (This is my sense from thinking about it during davening over several years. I don't think there will be anything too controversial here, but please comment if you disagree.)
- Maariv: Piyutim mostly describe our relationship with Hashem in the context of Yom Kippur, culminating in כי הנה כחמר
- Shacharit: Praising Hashem like angels
- Musaf: The avodah (and more praises at the beginning, with many of them focusing on the Beit Hamikdash, e.g. נחשב כצג באיתון and ויאתיו. I would like to think that all of them focus on the avodah but I haven't worked it out in detail.)
- Mincha: ????
- Neilah: Last chance, putting in as many י"ג מדות as possible. I get the sense that the piyutim are there as "fillers", to allow us to say the י"ג מדות again, and many parts of the selichot structure (פסוקי הקדמה, סלח נא, most of the ending pieces) are not there anymore.
Chazarat hashatz of mincha is basically the bare minimum relative to the rest of Yom Kippur, with the standard brachot and viduy but very little else, so there's not much to grab onto there.
How do the few additions to chazarat hashatz connect to the arayot and Yonah? What theme should you concentrate on during mincha?