Anytime you attempt to make a huge process shift you are tempting fate and risking failure. The short term drawbacks to huge change can often stifle the process before it reaches maturity. The trick is to work through the rationalization with the team based on current observable problems and lead them towards self-realization and analysis of their own problems.
Most people have ideas of how to make things better, but if you lead them towards the desire for slack, optimizing for the bottleneck, rather than maxing out everyone as if they're all the bottleneck, then you can easily get from there to Kanban-like WIP limits. From there you can adopt other solutions as the problems they tackle are realized.
Smart people frequently arrive at similar approaches whenf aced with the same problems, but not always. Your team may find some novel approach that works better for your context, or they may go looking for options and find Kanban. But the goal should begin with being able to communicate process problems, ask how they can be improved, test the potential solutions, and adopt the best ones.
Unfortunately, the biggest hinderance to gradual process improvement (once your team is on board) is that software tools tend to offer a "whole solution" and don't have the ability to grow with your team's maturity, unless they're writing it themselves.