vespa only? YES
amigo, there are other options there, how ever it can be done.
There is a guy here that has a 250 and has driving from Canada to Mexico and back and has no complains at all.
The question you have is very valid, I think the pump problem is a know problem and maybe there is like a year model or series that has that problem (like some GS650G, or KLR 08-09 and such) Maybe go to modern vespa and ask the vespa users there.
I would take the vespa I had and then just have it service, all the way to the valves, rollers and such. I have a KLR that has carburetors and I have had zero issues, so I would take the 250 if I had it simply because any way you will be stuck where ever waiting for parts since I really dough a vespa dealer would be there with what you need, I don't even there is an official Vespa dealer outside MExico city or Monterrey (the 2 biggest cities in Mexico, the BIggest country from here to Panana)
I DO get it about touring on a scooter to Latin America, I would like to take my scooter 100-125 cc down to Cancun from Ensenada so little wheals will be a thing to consider but the GT250 I drove has so much better suspention and bigger 12" wheals (my 100 cc honda has 10")
A motorcycle or scooter always turn a bad day into a great time!
KLR 650, Honda Beat scooter!!