So, I've been in email correspondence with a gentleman who sells Spykee batteries. Not standard, stock batteries as shown here:...but rather, similar packs with the same voltage but vastly greater amp hours. As Spykee uses a pack format common to most RC cars, it's possible to swap in higher-end batteries provided they either fit in the same recess, or can be made to fit with minor modifications.
According to this guy, the standard upgrade is from 1.8ah to 2.5ah. That gives you a driving time of around 3 hours. However he's looking to get his hands on some 13ah (yes, that's 13,000mah) batteries that will fit in the same spot with a small amount of case modification. Nothing drastic, just sawing away at part of the battery enclosure. Assuming the operating time doesn't scale perfectly with battery capacity, a conservative estimate of how long you could operate the robot on a single charge using a 13ah battery is 15 hours.
Of course it would also take much longer to fully charge. These are NiCD batteries, which have to be fully discharged before recharging or you get the dreaded "memory effect", but the robots will be in such demand that I don't anticipate that will be a problem. With the stock charger we'd be looking at perhaps 8 hour charging times. Why is this preferable to 3 hour charging times, you ask?
Well, because provided people are courteous and don't use the robot for too long, there'd be a bigger 'buffer'; you wouldn't have to worry about logging on to find the robot's out of juice, simply because it'd be awfully hard for anyone to use up the robot's entire charge before it got dark. And it'd have just enough time to fully recharge overnight. This means less time spent sitting inactive in the charging dock during the day, and more time being driven around.
Coincidentally, it's also possible to buy an extended use battery for the mifi. It ups the usable time from 5 hours to 15 hours, essentially the same as the robot's battery life. Unfortunately I can't work out any way for the mifi to recharge when the robot is docked, or I could mount the mifi on the robot itself and it would effectively have no range. It could stray as far from the dock as it's batteries would take it. This is a tantalizing prospect and I may do it once just to see how far a journey I can take the robot on before it's batteries die, but for everyday use I'll probably keep the mifi on the docking station so that people can't get too far from it.
The area I've chosen has 4G coverage, and as I've heard Spykee is somewhat laggy over 3G, I'll be buying a 4G mifi. The best deal I can find has a $60 monthly fee, which I can't really afford, so while I rejected earlier suggestions that I monetize this project, I may have to require some small form of payment for the robot's use just to keep the connection operational. It will most likely just be a "seriously, please donate" button at the upper righthand corner of the robot's website though.