Just within the last week, I've had a major (bloom?) of a reddish-brown algae. It now covers over 2/3 of my one acre catfish pond.

Times are tough here in East Texas. Severe drought. Pond is down abou 50%. Deepest area is now only 5'.

I do have a recirculating pump dropping water back into the pond adding some oxygen.

What is this stuff, and what am I up against?

Your reddish brown stuff is very likely algae. The evaporation and decreasing water volume are concentrating nutrinets and minerals in the water. The changing water chemistry is creating new conditions for a new algae that 'likes' the new water quality. Algae species change with changing water quality conditions.