First of all congrats on the beautiful family and the success you've had so far. I like the saying, control 1 million, own 1 million, make 1 million. You've now owned 1 million and are cash flowing so that's great. One thing to consider is tax increases. (Of course rent will increase with inflation and maintenance etc..)
You're in a tough situation because 5k is decent money. Enough to pay the bills, but you're still putting yourself and your family at risk. Because you have set the bar to JUST barely making enough to live on. If something happens you will be forced to sell, pull a HELOC etc.
You're obviously a smart guy, based on engineer background and ability to dissect your situation. But I would do what Brandon turner did and keep working until your cash flow is double what you think you'll need. The more you buy now the happier you will be in the future.
Also, living below your means got you to where you are now. But that's no way to live a life. We live in an abundant world. You and your family should have the privilege to access that gift. Don't live below your means, expand your means!
(Doesn't mean driving Ferraris) but it does mean being so frugal you don't buy the bottle of wine you truly want. Or you don't stay a few days longer on a vacation spending time with loved ones because changing flights will cost you 1k more. So you end up sacrificing. If you have the ability to sacrifice on your wants needs and desires and the ability to have them, why would you ever choose the former?