I was hoping this thread would answer this, but it didn't.
Are any of the new batteries considerably lighter or smaller than the dvd batteries we've been using to power the v3?
Yes and no. From my experience refurbishing batteries, the weight and size of the battery is taken up mostly from the cells. I think I read that Li-poly chemistry has a better power quotient (or whatever it's called) than Li-ion, but I also think I read that it's not by much. That means that, in general, battery technology hasn't changed much in terms of new chemistries resulting in smaller batteries that have more stored energy than the 18650 type Li-ion cells you have in your DVD battery.
So yes and no. Yes, you can buy smaller and lighter batteries than the DVD battery. But no, you shouldn't expect proportionally longer run-times. The smaller the battery physically, in general, the smaller the capacity will be. Not a rule, but a generality. Look at the specs of the battery you're considering and compare the specs for physical size and capacity with that of the DVD battery for the definitive answer. You'll want to figure that into your purchase of a new battery. You can also consider sending your old DVD battery to me to refurb with new cells. It's usually a cheaper option than buying new and the cells I've been using increases the capacity of the original DVD battery.