Instead of a cooler - try a dry bag for stuff you don't need instant access to. You can have dry bags on front and back of scoot and then put stuff you need a lot in some sort of compartment between your legs.
https://tinyurl.com/y56gqfjz
For the mount - I use the RAM iphone mount. You can attach to mirrors and you're in good shape. And then when you're done, buy the suction adapter and use it in your car to attach to the windshield.
https://tinyurl.com/yxtq7ffd
You can have dry bags on front and back of scoot and then put stuff you need a lot in some sort of compartment between your legs.
Try and find a 12v usb plug - you'll need to wire this directly into the battery - do not go off the device that generates power off the generator or whatever the vespa uses. Run the line from the batt directly or chase down a power source near the gauge cluster that only supplies power when the ignition is on, but the engine isn't running. Or make it real simple and get a decent USB power pack and just put it in the front glove box and power the phone with that. Charge it up at night or when you stop for lunch.
No need for additives - just change up the fuel like to the clear racing stuff and throw an inline filter in there. The fuel goes a very short distance and with the racing lines it won't degrade with ethanol. I'm against almost all additives - unnecessary. But - you do you
Practice removing your carb and partially disassembling to clean out - the top screws so you can access the needle/slider and the bottom float bowl. Carry extra zip ties and the tools you'll need to do this. Also - remove and replace the exhaust - it takes finagling to line up and you'll need some allen keys. (You have to remove the exhaust to get the rear tire on and off)
Also - practice taking the plug in and out. This is a PIA on these bikes. My system utilizes a spark plug socket 1/2" used along with a 1/4" adapter and a 1/4' small ratchet. The tool they give you is really hard to use in my opinion. Have a $3 spare with you - these take an odd spec you might not be able to source so quickly.
These things are tanks, but you never know what might happen on the road, so be prepared - if you do all these things in your garage you'll know how to do them on the side of the road. You can pare down your tools appropriately.
Might want to invest in a louvered engine access panel for cooling (or just remove it) . . . it gets pretty hot in there. The CDI's (coil is included) are known to fail, especially with a lot of heat. You are going to be stressing this engine - summer temps, high weight and long miles - keep it cool as best you can.
Go on ebay and buy a used CDI for $34. Install and make sure it works and if yours fails, you have a cheap backup and when you're done you can ebay it back.
keep us posted and send pics!