Sub domains are considered as separate and totally different domains in the eyes of Google. The SEO impact of this is that it will be like you are migrating to a new domain name. Any way you do this, you will lose a little of the authority (PageRank) on the other end. Same with 301 redirects.
So, we know you are going to lose a little, which is fine. You will probably not notice. What you need to be concerned with are general SEO best practices. Treat this like a real site migration.
Map out all of your current URLs. Redirect each URL example.com/widget/ to it's new home whatever.example.com/widget/ with a 301 redirect. Do not just redirect all old URLs to the root, or one page. You have to redirect each old page to the new page at it's new home.
I would stay put at your new location and not continue to move around. I did an SEO audit this past year where a very large company did exactly what you did, over and over. At some point, it will affect your rank more severely.