Given the way you have described your situation, I would say you have the following challenges -
- Too much demand (work) on your teams, across multiple products/ projects
- Constrained capacity to deliver. Your teams have not only planned product features to deliver but also a lot of unplanned work that comes up on a regular basis
- Unrealistic/ optimistic Sprint planning leading to Spring scope not being delivered
- Too many dependencies between teams and due to other possible external factors
- All of the above leading to dissatisfied customers/ management and poor team morale
In this situation, it seems to me that the Kanban Method will really be very helpful to implement. Here are the following ways you can use it to streamline your flow across the entire system, set expectations with customers/ management and help teams deliver based on their natural cadence. Over a period of time, Kanban will help you identify and eliminate bottlenecks and improve throughput, thereby helping your teams deliver more product features.
An important aspect of implementing Kanban is to implement it in the Upstream processes of product/ portfolio backlog management and ensuring that the right features/ stories are prioritized at the right time and scheduled on a regular cadence.
The second aspect of this would be to look at the actual nature of the current demand on your teams. This is comprised of both value demand (new features) and failure demand (issues/ bugs/ etc.) - as also intangible work such as tech debt. You need to identify the various components of your demand and provide for adequate capacity to do this work - and thus identify the true (net) capacity your teams actually have to do new value add work.
At the risk of jumping into a solution without further discussion, here are some suggestions.
Using the STATIK approach (Systems Thinking Approach to Implementing Kanban), you should consider implementing three levels of boards - Portfolio level, Product level, and Team level.
The Portfolio and Product level boards will help your stakeholders prioritize and coordinate work across multiple products and strategic priorities - and ultimately help your teams get prioritized backlogs that they can work on without confusion.
The team level boards, combined with WIP limits, will help you streamline the team level work - by helping identify specific points of cross-team dependencies and bottlenecks within their own processes.
One key thing that you already have said - instead of committing to a sprint/ release scope up-front, simply decide on a sprint or release cadence (2-3 weeks - a month at most) - and release/ deploy whatever is ready every3-4 weeks. Use the pull mechanism to take whatever is the next most important thing from the prioritized backlogs.
As you probably already know, there's a lot more to Kanban than just a board and stickies on the wall! If you need more help on the Kanban Method, please read up here. For more on STATIK, here is a great article. Third, please see this article on Kanban Flight Levels, which helps you model Kanban boards at multiple levels. (Since it was originally written, it has been updated and now refers to 4 levels of boards.) Finally, there is a lot of great training options at Kanban University.
All the best!