The first insight is that something needs to be done.
You can already now see lots of possibilities. Things that you sense could be done better or differently using digital equipment to connect the value stream. Or things that you see that your competitors do that you don't.
The worst reaction to this insight would be if you shout further down in the organization to start do all these things that you see needs to be done: "Start more projects! More digitalization! Why are you so slow?"
Instead you can meditate over the second insight. What you need is the organizational capability to invent. To look at your value streams in a new light. Can design thinking help? Probably. Implementing design sprints? Yes, that is one specific thing you can work with.
Or why not invest in an innovation center? A place where certain people in your organization are allowed to innovate, free of the constraints that reigns in the rest of the organization? Allowing two "modes" of operation in different sections of the organization: one fast where all the cool things are done, and one slow, where all your normal dull and slow and not so innovative people can do all the normal dull things.
While working "bi-modal" (as it is sometimes called) can be a starting point, it is definitely not a solution. What you could (and should) use it for is to let it help you get the third insight.
The second insight was that your lack of digitalization ability isn't caused by a lack of digitalization projects. The third insight is that your lack of digitalization ability isn't caused by the lack of innovative people or innovation centers. It is caused by structural hindrances, systemic factors, that you are responsible for upholding.
Organizations need structures that prevent them from falling apart. Organizations, just like organisms, must possess the capability to prevent too much change to happen at the same time. They must possess what biologists call homeostasis. On the other hand: the biological term for total standstill in the organism is death.
What the third insight inspires people to do is to invest in the organizational capability to move rapidly but with preserved integrity. Innovation centers can be organizational prototypes where those capabilities can be developed, but if the capabilities stay there, the innovations they might come up with will not affect the rest of the organization. Your core value streams will not develop.
That organizational capability is called business agility, and the ways of implementing it are well known and investigated during more than twenty years. They are neither hard or easy to implement, rather medium hard, but they involve a critical look at the present structures, including leadership culture and high level financial KPI:s.
The third insight is that you, as the leader of the organization, must start with yourself and think about what kind of organization you want to lead.