In Shemot 32:20 Moshe grinds up the golden calf into water and makes the people drink it. Rashi comments on this:
[Those who practiced idolatry both] without witnesses and without warning [died] from dropsy, for the water tested them and their stomachs swelled up (Yoma 66b).
That sounds like the same means of death as with the sotah ritual for the wife suspected of unfaithfulness, and according to here Avodah Zara 44a makes the connection. If I understand correctly, the g'mara says that and Rashi alludes to it.
The sotah ritual involves writing the divine name and then dissolving it into water for the woman to drink. I don't have sources for this, but it seems key that the use of the divine name -- that is, invoking and involving the One in whom she should be in fear and awe as part of the ritual, when otherwise we would never erase the name like that -- is critical.
But the calf is just a lump of ex-jewelry. It's not divine; it has no power at all. Grinding it up into sotah-like water doesn't evoke the same image at all. Why would Moshe want to invoke the so-called "power" of the calf in such a ritual?
What am I missing? Aside from the drinking part how is this like the sotah? Or if there are other opinions about why Moshe did this, what are those opinions?