I'm not getting enough clarity off of those photos to really pin it down... but you mentioned that the spots were small, and they look quite dark. Is it progressing just a couple of leaves at a time, rather than by leaps and bounds?

Fungal spots tend to show up so fast it's breathtaking, especially in wet weather. If it's going slowly enough that you can note which leaves get it and when, that suggests a bacterial disease. If the spots are also pretty consistently small -- 1/8" or less -- I'd try treating for bacterial speck or spot, and see what happens.

Pick off the worst leaves, as they won't get any better, and throw them in the garbage can. Then pick up some fixed copper spray from the hardware store or nursery, and spray them as directed (or as close as you can -- I understand you guys are building arks out there). If and when the rain settles down, you should be able to get a handle on it pretty well.

I'd suggest mulching just on principle, but I'm guessing plastic tarps might be more useful right now. Soil splashing up onto the leaves just makes matters worse; once the bacteria or fungus has a foothold in the lower leaves, though, it spreads upward by water splashing on those leaves.

--Alison