If you are dropping sectors, then you are changing the route and thus the ticket needs to be reissued. This means you need to pay the US$125 change fee, any service fee charged by the airline making the change and any change in taxes/fees/surcharges (ie, the fuel charges that have increased since you got your ticket).

You will be better off just changing the dates/times of the LHR-DXB flights and do a turn. It takes less then a day (I did a LHR-DXB-LHR turn last year).
BA107/BA106 depart LHR 1250, return 0620+1
BA109/BA108 depart LHR 2140, return 1400+1
This may require a ticket reissue, but should not cost anything.