I tend to imagine the eng out scenario cruising over FL300, but it can happen during the climb, at 9.000, for instance. Then the strategy to adopt is really important.
In the cruise, you are suposed to be able to fly 2,000 higher than any obstacle, so no need for an obstacle strategy, no need to fly slow. Otherwise you would have to determine decision point/s and/or escape routes and fly the obstacle clearance strategy in the event of an eng fail and then go, turn back or divert to a escape route, as appropriate.
So my view of this is: if there are no decision points nor escape routes determined for the route segment being flown jusf follow standard strategy. If there are decision points, follow obstacle strategy untill clear of them, then standard.