OK, so lemme try and understand something. You guys were using PF, right? If so, why didn't you ask everyone before you started if they were familiar with what you wanted to achieve? Even if the description says so, communication can be the key difference between a good and a bad run. I've seen many cases where a quiet party would get wiped pretty easily in content other than the ones everyone's talking about here. As soon as people started communicating and explaining mechanics, it all worked out. Low DPS is easy to spot without a parser, indeed, so what's the problem with suggesting a minute or two so that people can better understand what the party intends to achieve and perhaps google their rotations?
If you know someone is not doing their rotations properly (ofc, assuming you know the class they're playing), suggest a change. When I started playing someone pointed out I should use Bio II --> Miasma --> Bio instead of whatever I was doing. It was fine, they just said "just a hint, but you get more out of this combo instead of what you're doing." More recently I was partied with two players who had such awful DPS, it was difficult to carry large pulls bc mobs wouldn't die as fast as they should. The girl was SMN and since SMN and SCH rotations are somewhat similar (at least below 50), I gave some suggestions to what she could do. Unlike myself, who took the advice and improved my playstyle, she completely ignored me and continued to do what she was doing. Neither you or your friend seem to be people who will say "are you stupid? You're not doing your rotation properly, you dumbass", so the chances of someone getting angry at you won't be as many.
FFXIV has an amazing community, but just like every other game or any community of any kind, it has its bad apples. Skipping the opportunity to instruct someone for fear they'll get angry at your knowledge doesn't seem to be a good approach. You will never know how a specific person will react unless you try it. But ofc, if you do call yourself "elite", then that could be a problem. Perhaps try omitting that fact, as even skilled players who don't consider themselves part of any elite (and these people exist, they just so happen not to care about such titles) will likely stigmatize you for saying you're better than anyone there. Should you have a really high rank proven by official means, then sure, you are part of an elite and can call yourself such. But if you do, know that a lot of people will perceive that as arrogance and their reaction might not be the friendliest.
Also, as Eloah said, suggesting that the group should improve is more encouraging than calling out one individual. In your particular case, the group was indeed the problem. Your PL would probably have noticed the low DPS of one or two members, but apparently, all of them weren't as good as either of you expected.