I think you're better off concentrating on performance of actual problems versus memorizing definitions or theorems, when teaching math for general STEM. It is much more lasting to anchor something like exponent laws by doing problems with exponents (and being tested on them), versus just regurgitating them. In addition, much of math has a heavy algebra component and this is a weakness of kids. So, problems that require them to use several lines of algebra properly are a feature, not a bug.
I wouldn't completely stay away from "concept style" questions. But don't make them the main objective. So, for example, students learning second order constant coefficient equations should be tested with the ability to do a multi-step problem (abstracting the characteristic equation, solving the quadratic, maybe dealing with repeated roots, finding the particular solution if it is a heterogenous, and even perhaps finding the values of the C1 and C2, based on initial conditions.). If you want to ask a question about under/over/critical damped, fine. Makes sense. But that's a little garnish for the stew. The main thing is they need to be able to solve for y.
And yes, doing all the darned algebra involved in that, and properly. This will be needed/expected in their electrical engineering classes. It's OK and even optimal if you push the math problem first, rather than an electrical or control circuit. That should only be brought in later after the student has shown the ability to manipulate the math itself. Then (if there is time), they can later learn about how capacitors work different than inductors or what the heck a dashpot is. And if you don't get into it, they will get that in their majors courses. But it will go a lot smoother if they already have some familiarity with the ODE, while they are learning the physical components.
If you must push the concept stuff, there are ways to go about it that are a little more fun than recitation. T/F questions. Evaluating drawings. What has to be right for this relation to be true. Fill in the blank. Etc. But I would urge you not to jump too deep into "higher order concept" land and omit the needed work on solidifying their basic skills in the content. For one thing, these concept questions can be very logic/verbally demanding (the SAT question stuff) that ends up being a bit of a general intelligence test at keeping track of double negatives or divided by zero exceptions or the like. It's not that those are completely unimportant, but I just wouldn't emphasize them at the expense of normal calculations.
Of course in a class on logic or proof writing, the whole point is to learn to be careful about language and conditions, so fine. But this is not the case in most of the algebra/algebra 2/trig/analytic geometry/calculus/ODE/PDE coursework of an engineer. And even their (rather limited) needs in linear algebra should be more demonstrated hands on in terms of manipulating matrices versus proofs (and certainly versus tricky questions).
In particular, if you are teaching kids that are below elite (not CalTech, not Thomas Jefferson), it's probably especially important to be more traditional. They need the practice in multi step algebra. It's not trivial to them.