After thinking a while, I have a few ideas.
1) Rebuild the mowing deck. It just seems to be sucking up way too much power. Clean up the bearings, repack them, adjust anything that needs it and tighten it all up. Heck, the thing is almost 40 years old! Sure can't hurt.
2) Play with voltage. Possibly go to 48V. I'm not really sure I want to do this though.
3) Like Jim said, tow a trailer with batteries. The previous owners of my house were kind enough to leave me one actually, so this isn't a bad idea! But, this wouldn't allow me to use it for other things like yard work... trade offs, whatcha gonna do?
4) ? Still thinking.