Very exciting! And I can see why you want it perfect. But even it wasn't going overseas for such a special recipient, a few twisted seams wouldn't be the end of the world.
And next time you're making a quilt with a ton of pieced blocks that are going next to each other, the time to think about how you're going to press seams later on is when you're pressing the earlier seams. And you can see how the orientation plays a big part in the construction too. It was a big improvement for me when I started planning early on - the quilt tops went together faster and more smoothly because there weren't all those little hassles to deal with.
Don't second guess your choice to do the 4patch blocks. I think they make the quilt!
It will be beautiful and loved and appreciated and treasured in a way most of us can't even begin to comprehend.
Looking forward to seeing the completed quilt before you ship it off.