What is the most innovative idea to map the competency of an Organization with over 300 Management Members and 5000 Executives, Staff and Workers?

The Simple Idea is to involve the lowest hierarchy employee/worker  in an organization while making a organization strategy.Because great ideas often comes from the least important persons. 

Organizations do competency mapping in multiple ways : Despite the large numbers (few100s &1000s)that you have mentioned, there will be a groups of people performing homogeneous/ identical tasks & hence sharing identical competencies (though gradient of competency may differ).
so net net you will just have to do mapping for the probably maximum of100 such groups who will share similar competencies.
For workers it is largely skill matrix rather than competencies = Knowledge + Skills+ Attitude.
The multiple ways that organizations engage in the process are:1) Role Set based competency Mapping in case you are doing this internally.2) Card sort method is the easiest of one & the process can be completed in a weeks time- In this process the internal consultant or external consultant engage with leaders to understand the business scenarios that companies may face in future ( at least for next5 years).
based on this discussion + market (industry) intelligence , the consultant comes up with a3 or4 sets of cards( with14-15 competency names).
The leadership members are split in team and they internally discuss and rank these competencies in order of importance to organizations.
The competencies unanimously decided by the leadership team are kept aside and wherever teams differ in views are discussed in depth before arriving at the final competencies.
This is how an organization competency or core competency of an organization are developed.
Once competency is determined , it is defined in terms of behavioral indicators ( competency dictionary) so that the employees can follow this competency in 'letter and spirit'.
The dictionary will also have progressive gradients in terms of levels wherein it will be applicable from junior level to senior level.
Eg : competency:Striving for Excellence: Level1) Do the alloted job on time with100 % accuracy( as expected from a junior staff) Level2) continuously improve the quality of delivery ( as expected from mid level staffs) Level3 ) Create new or productive ways of accomplishing tasks.
I hope this clarifies.