N.Y. State: How to hack the healthcare system AKA how to have a baby for cheap?

So my wife (a stay at home mom) is on my insurance and im looking at 4300+ in costs between my deductible and out of pocket max next February. This does not include the amount I pay for her premiums. Yeah, I can use an HSA/HSA but I want to save a lot more than that.

So far I’ve gone to the NY state of health website and my thinking is, if I can sign her up for healthcare in January, pay a high premium for health insurance that covers most of the birth costs and do this for like Jan-Mar, if the premiums are 500 bucks or less and cover almost all of the costs of childbirth, then once kid is born, I can put my wife back on my cheaper health insurance. this could potentially save me 2000 bucks.

We gross 71400 a year and already have a child, so i should be eligible for a few hundred in discounts on the health care premiums.

Any other strategies you can think of? I am still searching health plans using this years data just to get an idea of what to look for this winter.

EDIT: Before anyone suggests waiting until we can afford another baby. I can afford to have and support the child, I am just a cheapskate 🙂