FCOM 3 may not be the bible (at least for the majority of us) but depicting SOP like general guidelines, there is a step I would not take
I never imagined that "WHEN LANDING GEAR IS DOWN" could be subject to debate.
But I got your point, don't worry. There is no such restrictions preventing you to operate both systems at the same time in normal ops.
I think it's only good airmanship as flaps/slats and landing gear are both hydraulic heavy load users.
Why would you rush that? To stabilize asap?...
