"... something to be passionate about is the main thing I lack in a job."
This is backwards. A job generally won't give you something to be passionate about, passion comes from inside of you. Passion is the thing you choose to do when you can do anything, passion is the thing you invest in when there is no obvious 'reason' for doing so, investing in your passions is its own reward.
Small anecdote, worked with another engineer at Sun who was struggling, and he asked me why it seemed so easy for everyone else and so hard for him. We talked about passion and its not 'easy' for someone who is passionate about something but it is 'fun' so they exude happiness digging into the problem not pain. At its root there is a attitude difference, just like people who are passionate about fitness aren't excited about doing exercise, they are being excited about how this exercise is giving them new capabilities in fitness. They look past the means and luxuriate in the ends. That is following your passion [1].
The engineer I knew realized his passion was helping folks get ahead in life, he was always happy seeing someone get past a challenge an on to something more fulfilling. He ended up following that passion and last time I heard was living in Mexico helping folks build sustainable communities without the stigma of 'technology backwardness.'
Ok so back to your observation, there are lots of 'engineering driven companies' they make all sorts of things from sex toys to intercontinental ballistic missiles. Its a wide range and 'engineering driven' doesn't say a whole lot about passion other than solving problems. But if solving problems in an engineering context is what you like to do, then you might start looking at jobs for program manager rather than engineer. I don't know of course, I'm not you. But its a way to approach your question which I suspect would get you further down the path.
[1] A litmus test might be, imagine you've been in a car accident and you're paralyzed from the neck down. What thing did you wish you were doing yesterday before the accident? Lots of self help books suggest pretending today is the last day of your life, what do you want to spend it doing? Etc etc. The bottom line is people with passion make a difference, and folks can tell that in an interview from a mile away if you're pursuing your passion or just marking time.
What you don't say is what you want to do. What are you passionate about? You know that "just doing your job is not enough" so you start a side project, great how did you pick it? Are you more passionate about it than your current job, if not why not? You had complete freedom to work on any side project you wanted. Do you even enjoy programming? Why do you do it? Why not gardening, or auto repair, or architecture?
People who are passionate about what they are doing are 10x better employees than ones who are doing it for some externally generated reason. Ask yourself what you really like doing and pursue that. You've got a job (great) and if you discover your passion is something else use your job as a springboard to cover expenses why you develop enough runway to leap into what your passionate about. Don't try to do that at a start-up though, its really really hard to be passionate about something other than the start-up's mission and be successful.