Popay,
The FMC does not take into consideration the clean up.
The flaps are supposed to be up at the end of the 10 minutes - not fly for 10 minutes in the takeoff configuration at takeoff N1 and then clean up.
I don't believe that you have any option BUT follow the EOSID and I also believe that you cannot GUARANTEE that you can meet the SID climb gradients on one engine when you consider the level segment to retract the flaps.
Why is it that hard? Engine failures don't happen everyday, if you follow the EOSID everytime there isn't that delay where you decide what you are going to do - that delay may well kill you and your fellow crew and passengers.