Last year we moved from California to Roussillon. Shipping the bikes was a huge hassle. Fedex wanted over $700 per bike ! Other shippes, not far behind. That's what their agents told me. A bike box too big for USPS to handle. I'd contact a shipper like Mayflower before I did anything.
I too converted my worn out Scott bike over to a Cross Check frame. A good touring /commuting frame. Still has some of the old Scott original components, I long term intend to update. A solid frame. Good ride. Will you have the bike built up in the US or elsewhere.