This is excellent information, although I'm the last person who needs to be removed from an oversold flight, haha.
I'll certainly look into all your suggestions and will print off my online check-in tickets for LHR > KEF and KEF > YUL (and keep them stored on my phone) anyway as a safeguard. I guess this would be the most sensible thing to initially do and then simply ask a staff member what they'd like me to do once I get there.
No idea how I'm going to print anything off for the return trip, but hopefully I can get it stored to my phone or something.
This has been reassuring. Thanks, all!