As has been mentioned changing the rear tire on the modern Vespa could be problematic due to the need to remove the exhaust. You might be able to stretch 8000 miles out of a rear, but there is always the possibility of non-repairable damage requiring a change vs. simply plugging. If you find a 250 that was produced after the bad fuel pump run or has had the pump replaced with the new version that should not be an issue. Before heading out I would do a full service to include valve adjustment, new belt, new rollers, new tires and of course oil. I would plan on at least one oil change during the trip, most likely in a larger city where you would have a better chance of finding the correct oil.
As others have mentioned, a scooter with larger wheels might be a better choice and Modernvespa.com would be a good source for detailed information/opinions. A P-200 would be pretty much bullet proof but would require shifting and require at least one tire change on the rear if not two over that distance. The P would also require sourcing 2 stroke oil thorughout the trip, but should be easy to find along the way.
Sounds like a great adventure.
(I have a 250 Super and Rally 200)