I think if you want a Director or better kind of position in the technical side of any organization, what you need probably isn't necessarily more technical "depth", but a demonstrated track record of delivering value by proactively applying both technical and organizational/managerial skills to solve business problems (or capitalize on business opportunities; two sides of the same thing), preferably problems or opportunities that you identified for your organization. (You'll probably also gain knowledge, at a high level at least, of all the technical areas involved in that solution in the course of doing that, and you can dive into those more deeply if they are interesting to you, but they aren't the things that are likely to be most critical at getting the positions you seem to be looking for the industries you are interested in.)

And, of course, the people skills to sell an organization on both your past track record of doing that and your ability to do the same in their organization.