I am doing the same in April and am on the 13:20 from LHR, might be gambling it a bit, but not as tight as being on the 17:00 one, but there is a limit to how much time I can spend at ARN airport, or in the lounge...

If you want to go into Sthlm there is also the commuter train or the SJ train other than the express. Will be cheaper and slightly slower, but there is a fee for all trains leaving or arriving at ARN that you do not pay at other stations.