I was not aware of the min(price_median) .... that's new to me :)

From the test I have made like a year ago, when this was a new thing, I usually would wait out for the conversions to end and check the final results .... and in the final result the final_price is used that is the median of the median in the 3.5 days :)
Turns out this min(price_median) is just a temporary price to ensure more collateral is put in.

How is min(price_median) calculated? Is it just a single witness at the bottom of the list deciding this number? Is that too much power for a single witness to hold?

Its not up to one witness, since it is still a median price for one hour, collected from the feed from the top witnesses. But then it looks at the median hourly prices from the last 3.5 days (84 data points) and choses the lowest.

The way I was going about HIVE to HBD conversions is doing them only if HBD is above $1.1.

Kudos to you for learning it live and digging in deep :)