Hello Peter,
You either need to create a new K2 module base on the K2 content module or you need to modify your template's index.php and item.php.

The second one is quite easier and since you know your way around coding it will be a piece of cake.

First open you index.php and exclude all the sidebar modules from your item views.
Then open item.php and use the markup of your index.php. This meaning you have to include your sidebar inside your item.php and two module positions one before the extrafields and one after.

PS. There are a lot of snippets about modules and module positions inside this forum that will make your life easier.