ATC doesn't have our turn procedure
Generally, for runways which are used routinely by a particular operator, it is not uncommon (probably even a courtesy) to provide a controlled copy issue to ATC for the eventual event ....
meeting climb gradient criteria isn't the issue
Absolutely ... the aims are
(a) make sure we miss the rocky bits
(b) get ourself to somewhere ... from where .... the aircraft can either
(i) depart to the alternate, or
(ii) recover to the departure
aerodrome OEI.