Are there any other battery types worth looking at that may be easier to live with should the worst happen?
Most larger battery manufacturers offer some 'gel' batteries in their range. These have the acid in a gel/paste form rather than a liquid, so should the case fail they would be safer, but are more expensive than lead acid, so I've never owned one.
If you get a sealed, or maintenance free lead/acid type, you wont have a risk of spillage. .
The casings are very tough, but not indestructable, so if your net protects from impact, it should be fine.
I've owned many, but I've only had one casing fail, and that was when a battery blew up during a charging accident.