This strategy is so good.
I found that American has a starting location bias toward calendar resources, which is bad for tradition policy. Calendar resources require Bronze Working to cut down the forest. One more tech detour from Mathematic means higher risk of losing the Hanging Garden. In my most recent Immortal, I have to rush the Hanging Garden by cutting down several forests and buying several tiles before turn 80.
I think Stone hence and Pyramid are obvious choices, but I am no certain about Temple of Artemis and the one unlocked by Construction. Those two wonders are good, but the cost is very high considering we have 2 wonders from ancient era. The biggest problem is that 4 ancient wonders increase the cost of hanging garden by 60%, which would endanger the chance of getting that wonder.