I agree on your assessment of Gilbert Strang's courses. So many here on HN recommend Strang's stuff. However, he's kind of the victim of his own success. If you've taken LA in college in the last 10-15 years, or any online LA class like Khan Academy, they teach from a geometric approach like he advocates and pioneered. Therefore, you're not exactly learning anything new, just a different person saying it; which, of course, might help. But it's still LA for the sake of LA.

Mind you, they are very good, and out of all online courses I've seen, the questions are actually hard and make you think and understand on a deeper level. Every other course I've seen have simple, fluff questions, if any.

Tim Chartier of Davidson College put out a class on EdX called Applications of Linear Algebra. It's more practical, but I found Part 1 to be too practical and not enough math. It suffers from the opposite problem. Part 2 may be better, but I didn't make it through. Plus, I found his style to be a little woo-woo. You might have some success with it because he actually does talk about real world scenarios.

https://www.edx.org/course/applications-of-linear-algebra-pa...

I've actually looked at about half a dozen online LA resources that take different approaches. I should do a blog post about them one day.