Making the switch from delivery to strategy is harder than most people think. It requires lots of persistence and luck in being at the right place the right time in making this work.
Once you have some strat stuff, and it seems that u do, its important to really show them that you are hungry, driven, and good at this type of work ( which is fundamentally different from delivery/execution type work). Make it known also that you prefer strat over delivery work ( if indeed , thats what u prefer). GThesew things will all help to ensure that you keep doing strat and not fall back into delivery/ops work.