Hmmm, I'd think you could get it way below $1K/month without much trouble. Think of it as about an average indoor swimming pool or pond with some changes and they're FAR from $1K/month.
Let's see...about a 1KW pump would probably turn that over once an hour, put it in more of a glasshouse to get natural light to cut down on heating and lighting costs so you can just use say 3-4 250 watt metal halides. Insulate really well around it and rig up a (retractable)plastic cover out of the stuff plastic greenhouses are made of to keep the heat in and cut down on evaporation hopefully not cutting out too much light. Heating could be aided by some coils going up onto a black roof in black tubing to be heated by the sun along with just keeping the room fairly warm.
So,
1kw pump=24 kw/hr/day
1kw lighting=12 kw/hr/day
1kw heating(Guess)=24kw/hr/day
That's 60 KW/hrs per day at about $.10 per kw/h makes it about $6 per day. That's only $180 a month. May be dim on cloudy days and a bit cool most of the time, but doable. Unless I'm massively underestimating some things.