You have 16 flight segments and 1 surface segment. You can add 3 more flights to your 20 segment limit. As for back tracking, most of the airlines operate hub and spoke networks, so you do back track instead of more direct 1 plane service. At least with the segment based ONE's you don't need to be concerned about that fact.
What cities in the US do you plan to visit? You mention Seattle. Perhaps fly London-Seattle, then use some of your flights to go to Canada and other US cities before going to Panama via Miami.