no problem (no charge, at least not for rtw tickets bought in Europe, I am not 100% sure for tickets bought in the USA) to chagne segments, routings, dates (as long as they are allowed and don't exceed the total mileage).
The non used airmmiles for the ground transportation Ecuador to Quito will be added to your total mileage allowance.
How do you fly 'back across the UK from LAX to New York?, or whas that a typo and you meant across the USA? Across the USA (backtracking, after starting in MIA on the westcoast) is no problem at all.