Gary,
A solution for your needs is probably too expensive to be seriously taken in consideration... A rechargeable battery like the one in the picture has its limits. I can check carefully the specifications and tell you numbers, but it's appropriate to help in an emergency when a car battery is dead. I never tested the limits, but it's more that enough for a keyboard with built in amplifier and speakers (I've tried it with both my DGX 300 and Tyros + the Yamaha speaker kit for 4/5 hours and didn't run out of battery; the sound was enough for a small church). Another thing to consider is that the DC-AC converter can't deal with more then 200/300 Watt. It's indicated for laptops and all kinds of low consumption electrical equipment but not really for the needs you mention - for your reference its price was around 120 Euro.
-- José.