I was given AWS Console access to an account with 2 instances running that I cannot shut down (in production). I would however like to gain SSH access to these instances, is
This happened to me earlier (didn't have access to an EC2 instance someone else created but had access to AWS web console) and I blogged the answer: http://readystate4.com/2013/04/09/aws-gaining-ssh-access-to-an-ec2-instance-you-lost-access-to/
Basically, you can detached the EBS drive, attach it to an EC2 that you do have access to. Add your SSH pub key to ~ec2-user/.ssh/authorized_keys on this attached drive. Then put it back on the old EC2 instance. step-by-step in the link using Amazon AMI.
No need to make snapshots or create a new cloned instance.