I would recommend travelling to US First and then Down To South America depending on Budget.......I think both routes would roughly work out at the same price with maybe E to W a bit more expensive
Its faster to travel west to east .......but to be fair it is also way worse for jet lag from what ive found ......so positives and negatives to consider
-Its about 20k baht to travel single ticket Los Angeles from either phuket or bangkok
-Take a connecting flight and spend a few days in miami (Go to disneyworld, the new Epic Universal Park which just opened, watch lionel messi play lol) for 3-5k baht etc
-Then many Airlines flight dirt cheap to South American from Miami Airports, you could fly to Cusco, Peru (Macchu picchu etc) for around 8k baht one way If I remember correctly
-Check out tinki village near Ausungate mountain, near cusco, amazing hot springs and you can rent a room and drink beer in hot springs whilst looking at the milky way