I've hired about half a dozen ML engineers/architects in the past six months. Several of them have EE backgrounds. There's a good bit of ML that touches on hardware (think integrated cameras and similar) so it can be really helpful.
You're mostly on track with your plan to build something. You do need to demonstrate that you have the skill set, but building one giant thing isn't the answer. There's so much that goes into building a giant thing, that I can't accurately access your ML skills.
Ideally I like to see a lot of small things over a reasonable amount of time. Someone with a solid GitHub showing 6-12 months of paper implementations, weekend geez-wiz hacks and various other projects would go right to the top of my call back list.
Hope that helps, good luck with the job search.