Finally I have managed to move codeshare over to Umbraco Cloud using my free Umbraco Cloud hosting that I get with my MVP rewards.
It's been a few weeks in the making but I decided to make a go of it when I realised that we at work are going to be using Umbraco Cloud a lot more going forward.
I've enjoyed the process of moving it to Umbraco Cloud using the Clean Starter Kit, especially writing the script to scrape the content from the old site and the Import code to import it into the new site.