UA is simply the ticketing carrier.
If OP wants to make changes, he will need to locate available award space on other carriers and propose that to UA. Because there is no IRROPS (the schedule change apparently does not cause an "illegal" connection), UA has no obligation to change anything, but might.
OP should also understand that his new ticket will also need to conform to all ticketing rules because it would be voluntary change. Thus, if this changes a RTW itinerary and more miles/fees are involved, those will be for OP to pay (unless he can get UA to waive them).