Around 5 weeks ago I started the process of 301 moving our website like this:

website.net -> website.com
website.de -> de.website.com

I did the first part so far (website.net -> website.com) around 5 weeks ago and it went well and most of the links have been moved but google is very slow with removing old website index and by the looks of it will take another 2-3 months at least to complete the move 100%.

My question is can I do the second part now as well (website.de -> de.website.com) and move the translated version too or should we wait until .net to .com is completely done? The problem is that this way it would take way too long and we plan to do a site redesign soon on a new domain as well.

I was advised to first do the domain moving and then after a while do the redesign and url structure change.

Also, GWT does not have a support for moving website to subdomain, will this be a problem ?