Santiago to Miami is 3600NM, so G200 and Legacy won't qualify.
G300/400 will be cheaper to buy than the G450/550 but the operating cost will be the same as the bigger Gulfs. F2000 must be the LX version, the classic ones won't have the necessary range. 605s are now cheap on the market, and plenty of them, and cheaper than F2000. If you can live with a ''pig with lipstick'' at FL410 then there is not much wrong with this airplane.