Such good advice so far.
I have worked in a small, family-owned machine shop and got exactly nowhere in efforts to improve how things are done, in medium-sized companies where I needed patience to have an effect (but eventually did once people were convinced my methods had value) and currently a large organization with maddening bureaucracy and a glimmer of willingness to adopt my contributions... but whether they will stand the test of time is unclear as I am just a "little fish." But my trainings have been well received, as well as my work in Excel to make current tools and tasks easier - like capacity assessment for suppliers.
So I feel hopeful for your prospects, but I agree you should go slowly and gently. One thing at a time, where and when it's needed, and make it as simple as possible. If you have skills in Excel, make tools that are very easy to use so people don't feel they must instantly turn into gurus - because they don't. Ishikawa's 7 Basic Tools are simple, direct and can be leveraged to save money - because that's what it's about, making more money.
I would use simple language like "Wouldn't it be good to do less of XYZ so we could get back to better things like counting money?"

or something that appeals to them. I think my #1 takeaway from these 30 years is that one needs to address one's people as internal customers, especially if they have a stake in the outcome you're after.
Best of luck to you!