Yeah, the Barthomeloi have special Magic Circuits.
The hunting on red moon isn't for fun. She's just the only one who dares to take the unnecessary risks.
"Strongest known living human" is still several levels below "heroic spirit".
Aoko can fight with average Servants. Ciel can to an extent. So not necessarily severals level below. Barty is a way better magus than both. She could match Servants in the right conditions. Forget engaging physically with Berserker or going for sword fight with Saber, but the possibility is there.
Lorelei hunts Dead Apostle Ancestors (who are easily High-Servant tier) on red moons (where they are at their strongest) for sport
Simply put, she's the Bruce Lee of modern Magi.
She does but she mostly fights alone. As in 'take care of the nest while I'm going for the boss' kind of cooperation.
Also, I'm not convinced DAAs are "high-servant tier".
It's more of a matter of affinity and concept than raw power. However, the top ten are at least a match for the high end Servants and iirc, they are specified to be non-killable at this point by the Church. So it's a matter of who has the means to kill the other. For example, I don't think there are many HS who can deal with Nrvnqsr while he could swallow most of them.