You answered the question about the Jay Treaty. It's unfortunate that that doesn't quite work!
It's a conundrum you'll ultimately have to decide on. If you go the K1 route, you won't be able to travel to Canada or work until your application is approved. It is more costly, as you say. Are you prepared to be 100% dependent on your partner and unable to visit "home" until your paperwork is through? New baby usually means you want to share with your family.
If you choose the CR1, the advantage for you having the baby in Canada is you're familiar with the medical system and likely have some supports, be it family or friends. I understand baby's dad wants to be involved and the costs aren't fun, but at least you can claim EI in Canada and have your healthcare looked after while you wait. When you do enter the US, you'll be able to work and travel freely.
There is legislation in Canada that is in the works to allow second generation to claim citizenship, but as of right now, it's not. If you have the baby in Canada, the baby's children will (without the legislation change) be allowed to claim citizenship. Yep, its far into the future, but it's a consideration none the less.
Good luck!