Like sdr said, it never hurts to make an offer. The listing agent has to present the offer to the seller, unless the seller specified they didn’t want to see offers under a certain price. Be relentless about them showing the seller the offer.
If the selling (buyer’s) agent is giving you a hard time, fire him/her. It is YOUR money, and you have every right to decide for yourself what you’re willing to pay for something.
You’ve got nothing to lose…submit the offer and tell them it’s your “highest and best,” if that’s all you want to pay.