I don't know if you have ever thought of running. I know you said you have a back injury, but it engages the abs more than anything else I've known and is a highly aerobic sport. I also recommend that you work up to incorporating long slow runs as you'll burn down belly fat while enjoying traveling for miles overland. Try trail running if your body can't take the pavement. Study the rules on increasing your mileage though so you don't get injured; never more than 10% more a week and every 4th week ease off for what's called periodization. Most people who try running get a few niggles that won't go away (shin splints, knees etc) and then give up, and most of the time they just did too much too fast.
Be patient as you have to work up to the long runs and it will take months to see the slow progression of your body changing. But as the body leans in running your endurance increases, there is less load bearing on the joints and ligaments, you'll transform the stomach in the process as you drop the weight that you don't want. Very few ultra runners don't have washboard abs, not saying most of us want to go that far!
Diet is huge. There are a lot of great documentaries out there about eating nutrient rich foods instead of the cheap processed junk we now pass for food.(don't get me started). If you like to garden then heap on the vegetables! Stay clear of grease, opt for olive oil to cook with. Just a couple ideas, study up on this.
As for sit ups, they are not much fun. As Richard suggested, not saying they won't help...just not as important as diet. Core exercise is better all around anyway.
Hope this gives you some ideas.:]