Using the minimum of all the history of median prices provides the maximum degree of protection. The most recent median would be included in that history, so if that happened to be the lowest price, it would set the minimum and the collateral required. If another earlier price were lower, collateral required would be higher.

I'm not worried about this resulting in "too much collateral". Let's say the price doubles or even tripled. That multipled by an 2-3x overcollaterallization ratio would require collateral of 4x-9x. I don't see why people wouldn't post that for a short 1-3.5 day conversion period in order to make even a 1-2% profit, and certainly for a larger profit. The cost of posting collateral for a short time which you then get back just isn't that high. For ease of calculation let's say 1% profit, 10x collateral and 1 day of conversion delay. That's 0.1% per day profit on the posted collateral which is 36% per year not even compounded (compounded would be much higher). This is easily enough to motivate people to do it, and is somewhat of a worst case calculation.

You are correct since we don't know the real time price there is still a risk of undercollateralization. We need to set the overcollateralization ratio high enough to provide reasonable protection as you say, and also just accept some risk of loss in exchange for all the fees collected along the way (not necessarily just from that one conversion request; overall the fees may be quite profitable if overvaluation happens regularly).

Also

With a 2x collateral requirement, the risk for too low collateral would require the 3.5 day price to be more than 2x the current price (and the likely price at the time of the conversion).

Not exactly. That would be the risk of the collateral being insufficient to cover the conversion from the start (obviously very bad), but you definitely want some extra collateral, not just barely enough to cover the conversion. The latter still gives the blockchain a good chance of a loss and the converter a good chance of a corresponding gain (if the HIVE price were to drop still more during the conversion process).