Any quality 250cc scooter such as the Kymco ones you mentioned will be good for your 100 mile trip. I had a SYM HD200 which was good for 70 MPH and cruise at 60 no problem so the 250 will be just fine.
Also I would not worry about bikes sitting so long, maybe tbe carb might need cleaning.
Vince @ SWFL or WNC
2001 Kawasaki W650
2012 Ural Yamal
2012 Dong Fang DF250RTB