Would definitely recommend a late check out if possible, but FYI not all of the lounges at Logan have showers, they're generally fine but for your purposes you might want to double-check if you go that route.

If you're flying out of Terminal E (like most international flights), I think the BA and Emirates lounges are the only ones with showers. That being said, not sure if either of them do day passes. If you have a choice, the BA lounge is better IMO.