The thing about trans-Atlantic 737s is that at least if you're going east, the flight times can be quite short. I have done Boston to Gatwick in 4 hours 55 mins, and Newark to Heathrow with one orbit over Clacton in 5 hours 20. With a good headwind you could do Boston to Ireland in under four hours easy. It's getting back to the States that is more time-consuming. I'd love to do a trans-Atlantic in a 737, it'd just be weird but quite groovy. A320s are used from Scandinavia to Florida via Bangor ME, and I have flown in an A320 from London to Beirut and back, which is 5 hours and a bit westbound. Excellent flight both ways actually, with a tiny (one plane and one route at the time) airline called British Meditteranean, now a BA franchise carrier. The A320s are deployed by BMed even further afield, to Baku and Yerevan as well as the Damascus and Amman add-ons to the double daily Beirut flights.
fly Saha Air 707s daily from Tehran's downtown Mehrabad to Mashhad, Kish Island and Ahwaz