Sounds like there's lots of misunderstanding over what Agile is, which is reflective of the software development industry, especially in older organisations. A huge part of my job is grappling with this for a large company.
What I've learnt is that scrum isn't agile. Kanban isn't agile. Agile isn't a process that can be defined and adhered to, which is what most executives want sold to them by consultancies as that's the only way they can often think. It isn't something that can be easily scaled up, either. Scaling it kills it if you think of it just in those terms.
There is a big difference between Agile (with a capital A) and agility. Agile (TM) is what has been adopted by companies and consultancies as a way of working or process that can be sold to you with the promise of improving efficiency, lowering costs etc. Many companies exist just to sell this to organisations and it has created a whole industry around it.
Agility (small A) is a mindset and a set of values. Take a look at the manifesto for agile software development (unfortunately still using a capital A!). The values expressed here are old, but still relevant I think. If your teams can embrace these values, then you can become more agile and may see some of the benefits often claimed, such as improved quality, reduced time to market etc.
Individuals and interactions over processes and tools
Working software over comprehensive documentation
Customer collaboration over contract negotiation
Responding to change over following a plan
The thing is, nobody can tell you or your team how best to adopt these or design a process for it. The team must agree their own ground rules and continuously evolve this themselves by introspection, innovation and a continuous improvement mindset. There are some good places to start or draw inspiration from, but I wouldn't recommend a prescriptive methodology like Scrum(TM). Start with a simple flow based system with a backlog, chunking your work and getting better at estimating size and team throughput until you have some appropriate forecasting ability. Get closer to your customers, make sure you have an environment that allows you to get the best from every team member.
The most unfortunate part of this is that the real agility is not something that can be bought in or something you can tell your teams to do. With most company executives looking for an easy solution, the tendency is to attempt to buy this in or hire expensive coaches who will sell you their particular flavour of Agile (TM), which leaves most people in a worse state than where they started. I can't think of an organisation who decided to 'do agile' and either buy it in or follow a prescriptive methodology that I can use as a good example. There are, however, some organisations that developed it themselves and found that it could be great, but don't think you can just copy their methods as they most likely won't work for you!
EDIT: Worth also saying that my perspective here is one of software development. Other things can use some of these principles for sure, but if you try to say, use Scrum(TM) for contract negotiations or infrastructure deployment, you may find it even more difficult than something like a unified SDM methodology that would have been more traditional. Not saying it's impossible, but some methods are better suited to different things and only you and your team can figure out (by thinking or ideally, trying) what that might be.