I wanted to offer my recent experience as we were in Barcelona before and after our recent Med cruise on 8/12/17 (and also before/after the terrorist attack).
Our cruise ended on Sat, 8/19 but since I couldn't get flights home on that day with my points on AA, we flew home on Mon, 8/21 so we had an extra two days in Barcelona after the cruise ended on 8/19. Our flight was at 2:30pm and was direct to CLT.
We left our hotel around 10:30am and as mentioned, the airport isn't that far away so I'd say about 20 minutes approximately. Clearly we left when there was extra security due to the attacks and I didn't find it extra long or tedious. I was honestly more concerned about the strikes going on but either we timed it on a day they weren't doing it, or they had called in others to help which is what our hotel had told us would happen. It definitely did not take any longer than TSA at MCO!
For those not familiar with International flights back to the US, you do go through a few check-points with the last one being passport control. In BCN, they held people back in a waiting area until near the boarding time for the flight, then you show your passports and go to the area to board the plane. They were definitely pulling people out of the line for extra screening, questions, etc., but I didn't see those people taking too much longer.
All things considered, we didn't experience any issues flying home, no extra delays, it ran smoothly, etc.
I remember they started letting people off the ship around 7am and I want to say we were in port by 5:30am. We actually said when we disembarked it was the easiest and quickest one we've experienced and we've been to Port Canaveral, Miami, Vancouver, NYC, Dover, etc. We weren't in a hurry but I'd say we were leaving the ship by 7:30am and then easily found a taxi outside and headed back to our hotel in Barcelona.
I would be on the fence about a 10:45am flight so it would depend on my back-up options. If you can stay an extra night (which sounds like you made that decision already!), it is a great city, however for those reading along - it's doable based on what I've read and experienced. I'm not saying others won't have delays and other unforeseen circumstances which is why the earlier flights are always a gamble but I don't think it's completely NUTS to consider it!
Enjoy,
Heather