How is that view regarded within your institution as a whole? Would it be agreed with, or would you be a pariah? Who are the “impediments” to requiring higher level of ingoing prep, math prerequisites, etc.? Because I suspect your real problem isn’t at all your teaching technique - it’s that you’re being asked to make silk purses out of sow’s ears (metaphorically of course - I don’t mean disrespect to your students, but they don’t appear to be on the level to learn what you think they need to be taught).
I’ll also ask the question a different way. Whoever is the mucky-muck of the engineering tech program - do they agree that their students “need” the level of rigor you propose teaching, or do they think you’re providing overkill? Do they see you as an impediment to getting kids through the program?