The most important part of agile
The most important part of agile is the deliberate introspection that should precede the retro
People think about agile as an iterative and incremental way to deliver software. The real power is in the meta-process - the iterative and incremental way to improve the way you deliver software. Executing the meta-process effectively requires deep thinking about the current process, explicit hypotheses about courses of resolution, and regular inspection for whether the resolution is working. This level of diligence isn’t compatible with the usual way retrospectives are held (little to no preparation, limited time, immediately after the rush at the end of a sprint).
The second most important part of agile is the culture that permits suggesting and following through on real changes
Your teams aren’t dumb. If you are really only asking for safe, non-threatening improvements, that’s all you’re going to get. If you are asking for real improvements, but don’t follow through making them, then they’ll stop putting in the effort to find them.
Regardless of what actual process and practices you start with, if you are disciplined about the meta-process you’ll eventually end up converging on something effective.