So for whatever reason (the most likely being displacement by the massive amount of snowand rain weighing down my cover), my water level has dropped about 10-12".

My question: once opened (I know there is already some algae in there), do I take advantage of the higher chemical concentrations afforded me by the reduction in water volume and clear it up before refilling, or do I refill the water first?

The water is almost definitely below the skimmer, but running off of the main drain only shouldn't be a problem for me, unless there is some other reason for me to refill the water first. If I need to, I can refill it while closed by putting the hose under the cover, saving that time after opening and possibly giving me one extra swim day.

Any thoughts?

Six of one, half a dozen of the other. You don't want to try and fight algae unless you have the pump running. If you can get the pump running without refilling, then you can fight algae without refilling if you want. Sometimes it is difficult to get the pump properly primed when the water is lowered, especially if the pump is above the water line to begin with, but as long as you can turn off the skimmer(s), it usually it isn't too difficult. The down side is that high FC levels can shorten the life of the cover a little.

I don't plan to shock with the cover, but I can refill with the cover on. Given all of the rain and snow we've had lately, I'm sure we have a high water table. I think filling now would be best because bleach is cheap and all of the other balancing will have to be done anyway, so maybe waiting would only save me $10 worth of bleach. Given the risk to my liner and pool if I wait, it's not worth it.