It is a tall order to do what you want, but it sounds like others have made it happen. Cars paid off - check. That is a HUGE thing right there. You should be able to go a year without buying new clothes (possible exception of some necessary items) especially if the wife is doing the stay at home mom thing. She doesn't need fancy clothes for that. My wife and I make virtually all of our own meals. We get take out about once a week. Not only is it incredibly cheaper, but it almost invariably tastes better and is better for you.

I would personally avoid increasing debt if possible, but having the HELOC in the background would suffice for emergency funds since you don't have any in the bank already. I think reducing your expenses would be better. Do you NEED cable and a cell phone? That is about $100 a month right there. Or maybe just you with a cell phone as you will be traveling and your wife doesn't need one. Probably a bunch of little things you can do that will add up.

I'm getting ready to make the transition from military to airline and it is going to be about a 60% pay cut for me, but we don't have kids yet (intentionally waited until after this period of low pay), my wife makes good money, I'll have a reserve gig, and we have a stash of cash and cars paid off. I have been working on this plan for about two years though.