I would go after market for all the parts you want to upgrade.
1. Kelly Controllers or Power Velocity are good places to go for a decent motor controller that isn't limited or locked down. You configure them to how you want the controller to perform. Both of these companies make very small, inexpensive controllers that will work for this tiny ride.
2. The hub motor in the Urb-e is geared based on their web site. This isn't a great idea, adds noise, reduces reliability and loses efficiency. There are gearless hubs in the size you need that will blow your socks off and still not be expensive. While you are buying one of them for the back wheel, get a second one for the front wheel. The space taken up by gearing can be used for bigger stators and magnets for a more powerful motor.
3. I can't speak to your throttle. It may not be the problem at all, but rather the limiting factors in the controller that look like a throttle issue. I would pretend for now that the hall throttle is working fine and that the controller is the big weak link followed by the motor.
4. The top of the line model only does 18mph...weak...very weak! With 1 and 2 above that will probably be more like 25mph. After that, if you want better battery run time, just ride slower. If you want more speed, crank the throttle.
5. The battery pack is a limiting factor too. I have no idea what cells they use from Panasonic. There are so many options from any particular manufacturer that the name just doesn't come close to covering the possabilities. If I had an urb-e, I'd be looking at how I can upgrade it's battery pack. All the bells and whistles on the factory battery pack are just taking up space and limiting how much capacity you can have. They state 35 volts of LION battery power. That works out to either 8S (32.8 volts) or 9S (36.9 volts). The battery pack has either 48 or 54 cells in it, but not 50 like the web site says. 50 cells just doesn't work out into any combination that is workable. I get those numbers based on the pack voltage and the number of cells it takes to get that voltage and then the rest is just logical guess work. Anyway, I'd be figuring out how I can fit 10-12S in that battery box and losing all the internal crap in the battery box and down tube. More voltage = more speed!
6. I think the main tube has extra stuff in it that can be removed so that a larger pack could be installed in there. The factory pack is convenient in that it can be removed fairly easily. If you are willing to sacrifice the "easily removed" part of that equation, then you have more space for batteries to either increase the capacity or voltage. If the space can't be enlarged for more cells, then I'd buy whatever are the absolute best cells I can get to put in that limited space and build a pack. My expectation is that there is a good bit of wasted space. Also, the motor controller is up in there too. Move it elsewhere...like in the secondary down tube...so you can use the entire main down tube for batteries.
7. There's the basic model and the one with better suspension. I don't know which you have, but that back "honeycomb" frame that the seat attaches to and ends in the back wheel is just begging for more batteries to be put in it. Another option is to fit a pack that sits on top of the back "tube" so it doesn't interfere with the folding mechanism. There are clever places that a larger pack could be added that will still be functional.
8. There's no reason to buy the "performance" option. The better suspension and opened up back down tube that the Pro and GT share are important, but the so called "performance" mode is simply a slightly more powerful motor controller. $300 can buy 2 or 3 far better motor controllers than is in these things. The performance option is simply irrelevant to me since the first upgrade I would do is replace the pathetic motor controller they are using. The pro versions have 350 watt motors. Any 6 fet 1000 watt controller which will cost around $60-80 will work and they are very small. IE: the "performance" option IMHO is a giant waste of money.
9. The pro versions are better Urb-E. Bigger wheels, bigger motor space, better suspension, etc. I'm pretty sure I could modify one of these things and still have it look almost exactly like the factory ride and get 30mph out of it and 20+ miles range and be much stronger. It would be a bit heavier due to the larger battery pack, but still something like 45 pounds at most.
It would be a super fun project build and when done, will do wheelies without having to lean back at all and be able to sustain them easily. I bet that the factory motor could handle 500 watts and replacing it all together with one that isn't geared would allow for a 750 watt motor in the exact same sized wheel. I'm pretty sure that on such a tiny ride that it would accelerate like a small car. Two such motors, would add a good bit of weight and require more battery power, but it would also be very powerful and probably accelerate faster than most cars.
Let's face it, this little ride already looks a bit odd so modding it a little with an add-on box for more batteries wont change it's already boxy looks.