Gram,
Perhaps you've moved on already, but I have some thoughts on your Vespa conversion. When I started converting my 1961 VBB, I had no experience in EV's so I did some research into a European scooter made by a company called UNU. Since they don't sell in the states, I copied their specs and started putting the bike together. So the relevant part here is that I ended with a 52V battery, a 3KW 48V QS motor, and a Kelly Controller. For a short while, it was a blast but I could only go 30mph, which limited my routes to and from places. Skipping the cool factor of having an electric Vespa, it just wasn't fast enough, and 48V is going to leave you with a similar top speed.
The solution for me was to rebuild using a 72V battery 28Ah, 4KW 72V QS motor, using the same controller. You can skip this expensive step by going straight to a 72V solution with the biggest motor that will fit your application. My top speed now is 54mph and my range is 24-28 miles depending on how hard you ride the throttle. You'll have to find space for more battery if your goal is to have a range of 50 miles.
There are good builds on this site from members Scusi and JimVonBaden, both building a PX. My original posts were on ModernVespa under the name Resistor. These might give you a better idea of what is possible and save you some time and heartache. Plus, more power is always fashionable.