I got bored, so here's one route I made. 8 new countries with 1 underused country.
Leg 1: Boston, Massachussetts, United States --> St. Johns, Antigua & Barbuda
Leg 2: St. Johns, Antigua & Barbuda --> Prague, Czech Republic --> Bratislava, Slovakia
Leg 3: Bratislava, Slovakia --> Košice, Slovakia
Leg 4: Košice, Slovakia --> Ljubljana, Slovenia
Leg 5: Ljubljana, Slovenia --> Luanda, Angola
Leg 6: Luanda, Angola --> Kissama National Park, Angola
Leg 7: Kissama National Park, Angola --> Doha, Qatar
Leg 8: Doha, Qatar --> Naypyidaw, Myanmar
Leg 9: Naypyidaw, Myanmar --> Yangon, Myanmar
Leg 10: Yangon, Myanmar --> Vientiane, Laos
Leg 11: Vientiane, Laos --> Nadi, Fiji
Leg 12: Nadi, Fiji --> Seattle, Washington, United States