Now that the Atlantic gap will be closed.
WS (Westjet) is starting/restarting Canada-GLA and DUB service so it will be perfectly feasible to cross the Atlantic on a 737.
So far, I can see
DUB-YYT or GLA-YHZ with 737 connections on WS to YVR-HNL. FJ picks up with HNL-NAN-SYD, QF SYD-DRW, MH DRW_KUL-BOM, MS BOM-CAI-ATH, assuming FR flights are all 737 (website has no a/c info), then ATH-STN-GLA/DUB
http://www.gcmap.com/map?P=gla-yhz-y...X=720x360&PM=*