Hello,
My name is Alex Moore. I am the Analytics Department Manager at a large Google Analytics Certified Partner (GACP) company in Pittsburgh, USA. In the evenings and weekends I moonlight/freelance relating to Google Analytics (usually not on Freelancer.com, as you can see from my profile).
I have over 7 years of experience working on Google Analytics implementations and have been setting up cross-domain tracking for clients for years. I also train on GA and Google Tag Manager at public seminars all around the United States. I teach 3 to 4-day trainings on these topics, so I am well-acquainted with the ins and outs of these platforms. I have worked with hundreds of clients over the years, across all industries.
I looked at your website source code, and I can already see what is wrong. A one-line code fix *should* take care of your cross-domain tracking problem. I haven't walked through each page of your checkout, so I don't yet know what happens when the visitor finishes the steps (do they go back to the main website?). I will want to do a bit of digging before calling the case closed, but I am confident that I can figure out any problem relating to cross-domain tracking, as I always do.
Then I would recommend an audit of your existing GA/GTM implementation. I can already see other serious problems, as well as opportunities for additional events, custom dimensions, custom metrics, etc. You could be leveraging GA in a lot of cool ways, and I'd like to show you some.