Hi, I am very new to this site and to the world of infidelity (although I was actually in it, just didn't know it!) so my advice may need to be taken with a (huge) grain of salt.
I cringe like you do everytime my husband apologises, says he loves me, recognises the harm done. He is doing everything "right" now (though so slowly and imperfectly, with still lots of crying and guilt, shame etc, and a little teeny tiny bit of empathy and true remorse starting to show). And for me it's only been a few months after Dday (though years of hiding secret behaviors on his side).
The way I see the answer to your question (and I am scientist too so bear with my very "technical" response!) is that we as a BS have 2 choices in these situations: recognise that they are unbelievable and that it makes us suffer to hear them say these things now (showing they can and in a way knew all along!) and let them know OR offer them a space for "redemption" of some sort by "allowing" them to practice telling the truth though we won't believe them for now.
What I mean is that however you take these moments of expressions of regret, apologising etc (cringe inwards which only hurts you, lash out to say how hurt it makes you feel or let them speak it as a practice TOWARDS healing, reconciliation and fidelity), they are only ever for the wayward spouse in my opinion. They never actually do anything positive for us (except with repetition, over years and if there are clear consistent actions as well).
I have told my husband exactly how I feel when he apologises, says he loves me, he regrets the hurt etc, I let it be SEEN how it makes me feel and I have also clearly told him that I have no obligation at all to listen to him say those things but I have chosen to do so as a way for him to practice being truthful and acting upon the truth (so in a way it's my contribution to HIS path of healing and correcting his behaviors).
I have also told him that I do not believe him in those moments, I listen to him for his sake and ours because i have chosen reconciliation (so far) and maybe some day if he keeps it up, I will decide to trust him again and then actually believe him when he says it.
This is clearly spoken between us, he knows it hurts & angers me when he says those things (like all the things he confessed, it's all just this big bag of garbage to me, his words didn't mean anything then and so he doesn't get to have them mean anything to me right now, but HE is learning to give meaning to his words again and that some day will show!).
In all honesty, when he says those things (I regret, I am sorry, I love you and want to be with you) it helps me assess where I am at and how I am feeling about him (sad, anger, etc), and I make sure he knows it. Knowing he knows how I feel and acknowledges it, to the point where he understands that even saying sorry or I love you hurts me, knowing he is accepting that and working to move forward and everythin (and he no longer gets angry or defensive at all anymore), seeing that change in him gets to me very positively and is helping me to *start* building some level of trust, much more than any word he could say to me right now.