Reading "between the lines," I suspect that the organization may not actually be all that innovative, but rather, undisciplined without a clear sense of purpose and principles upon which to make good decisions that everyone can align and engage with.
IMO, the 80% project failure rather, isn't caused by a lack of planning, but a lack of deep foundational principles upon which culture, innovation, decision making, and plans of action stand. Discipline is about adherence to principles and those principles are much more than just profit -- they are about value generation in all it's forms and for all stakeholders.
There is a story about SW Airlines (not sure how true it is) that helps illustrate the point. SW airlines has a 'guiding question' that EVERY employee is taught that goes something like - How will this idea/choice/action help SW Airlines be 'the low-fare airline that people love to fly'?" If an idea or action can't be defended in this context, that's the end of it. The question turns a simple "guiding principle' into an action-value inquiry. Everyone, top to bottom, is held to account for their choices and actions against this simple question/principle.
What's your organization's, guiding principle?
Being the controller of a for-profit company, you and the CFO are in a unique position to help drive a more disciplined approach. Get the CEO on-board by showing him/her how the much the current situation is costing the organization both directly (profits) and indirectly (culture, engagement, lost productivity, etc.) and how little real value is being created by the current circumstances. Then explain how, establishing a clear set of core principles and guiding questions can help focus and foster good decision-making, innovation, teamwork, and cost-effectiveness.