Right... You missed my point, kinda. While Avalon lolnopes everything, the problem is that she herself is kinda inefficient against these two. She needs her strongest ability to even put a dent on one and to seriously injure/kill the other.
Herakles is fully capable of going toe-to-toe with her in close combat due to his extraordinary stats and skills. He can also snipe her via the Nine-Lives: Shooting Hundred Heads while she is unaware. While I don't think he would do it at first encounter because of his personality, after seeing Avalon or Excalibur(she cannot even pierce God Hand without Excalibur and Herakles is not going to sit and wait for Excalibur to be unleashed in his face) he will keep away from her, waiting for a chance to take her out.
Worse case, he may have to take out the master him/herself. Herakles will not like it but considering the shit he has done in his life, simply sniping another Hero or her master won't be the worst thing he did if it is the only way. And didn't Saber used Excalibur on Herakles and the latter survived it?(Heaven's Feel) I didn't read the third route fully due to not liking it but I think I remember something like that. If he is capable of taking that to the face and survive, he is going to be immune to it the second time anyway.
Karna... Karna is easily capable of keeping up with Saber in close quarters. Due to Kavacha and Kundala, she will need to bring out the Excalibur if she wants to take Karna down. Karna will not wait there and take it to the face either. That is the main problem. However I will give it to you that Karna's personality may keep him from going to sniping like Herakles would do in that situation.
Edit: I remember Achilles. He would be the perfect counter against her. He doesn't like Kings and you need Divinity to hurt him. He also is not that bad and actually has the potential to be a very good friend to his master if his master is a ''good person''. He has a soft spot for people he recognizes as good people I think.