Notice that I said "as the subject of a sentence". It certainly works in the single case you chose. How about these:
"… and me and Carl were quietly trying to weigh up which team …"
"Me and Carl had a winner and …"
"During the excercise me and a colleague, Carl, made ourselves available …"
Yes, those are incorrect. Perhaps it's just because I'm not located in the UK, but it really stands out for me. Those, the lack of periods and phrases such as:
>and thinked the way most of the team already worked and thought
Yes, that sentence in the first paragraph stood out to me too, but I really didn't expect for the article to gain traction.
I want to add that I can't suit everyone, there are things that annoy me about American English grammar that I can't change, and I wouldn't think about writing in the comments suggestions on how to fix it. Maybe that's just me.
"… and me and Carl were quietly trying to weigh up which team …" "Me and Carl had a winner and …" "During the excercise me and a colleague, Carl, made ourselves available …"