This is a configuration that lets any User work other people's Tickets. I call it "Work Tasks Assigned to Others - Open".
Download the attached PDF and follow along.
David Martinez Sr Software / Systems Engineer NRG Energy, Inc.
You are right, the 'Others Actions' are enabled by Can Administrate permission on the incident. The steps also work just fine.
However, in essence, what you need is an additional permission on the incident for users that need to do those actions. I would recommend doing this via permission instead of group. You could create a new permission (i.e. CanAdminAllIncidents), copy what ServiceDesk.CanViewAllIncidents permission is doing (similar changes in the workflow as you suggested, but for a permission not a group).
Then you could give the newly created permission to any group you need :)