I think splitting works best here.

I think we do that when it's natural to do so (奸邪: wicked person; evil thing). You can find some examples by searching the "Refs text" field for "また、その人" in the advanced search.

In this case I think it's more natural to split. Especially since the source word doesn't refer to bagging/sacking, the split helps to make this unexpected distinction clear.

We don't usually separate the action from the person doing it into different senses. (with some exceptions)

daijr/s only mention the 人 / 店員.
sankoku has 〈こと／人〉.

Might be better to lead with "sacker" if only because that's the source word

@@ -9,2 +9,2 @@
-<gloss>bagging (at a supermarket)</gloss>
-<gloss>sacking</gloss>
+<gloss>sacker (at a supermarket)</gloss>
+<gloss>bagger</gloss>
@@ -14,2 +14,2 @@
-<gloss>sacker</gloss>
-<gloss>bagger</gloss>
+<gloss>bagging</gloss>
+<gloss>sacking</gloss>

GG5: 〔商品の袋詰め〕 sacking; 〔袋詰め係〕 a 《supermarket》 「sacker [bagger, packer].
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