I made at least 7 or 8 offers in the last 2 weeks and most countered with something near $10 less per point. My offers were usually $20 or more below asking. I would not call my offers lowball. I would instead call them realistic. Anyway, I just kept plugging along until one got accepted. I was actually surprised since my offer was $20 less per point than the listing. I was originally hoping to pay even a bit less, but the contract is exactly what I wanted and comes with double points this year.
My advice, for what it’s worth, is to just move on to the next contract. There are 2500+ of them to choose from. Good luck