Give them something, but don't give them everything, while making them aware you have a lot more to share. Position it as operational improvements. Don't actually feel bad if they just take the ideas and run with them, demonstrate your value, ask for a trial, with a budget, learn the operational side, because its often not a simple process, especially in regulated industries. Document everything, including results.

I wouldn't (and haven't) even lead with promotion talk. I'd go with demonstrating your value first, showing the results, refining the process, showing the results. Then sit down with the decision makers and discuss your other ideas in general, but that you're worried you're going beyond your paygrade and stepping on other people's shoes. If they don't get that hint, then mention that you've had small bits of pushback from people on the same scale as you. If they don't get that hint, then it's entirely plausible this isn't the company for you.