I think actually re-assigning the regarding account might not be the best approach.
Have a look at this set of custom workflow activities: CRM 2011 Workflow Utilities
With this through a workflow you can share/un-share records to different degrees.
So what you could to is create the first workflow to run maybe when the service activity is assigned, it will use the custom activity to share the regarding account to the service activity owner.
Then a second workflow runs when the service activity is closed, it then un-shares the regarding account with the service activity owner.
You might have to go a little further with this - in cases where a service activity is assigned and then re-assigned you might not be able to un-share the account with the original owner because you will have already lost the option to find the first asignee when the assign event happens.
This might not be a complete solution but it might give you some ideas.