Just do it. Let go of the “personal.” If they reject it, they reject it. Until the deal is finalized, its up to the buyer as to how much they want to spend. The seller just decides how much they’ll accept. Your agent better not be giving you grief. If they do, I’d find another more competent agent. They should say, “well, here’s how it might be received… but I’ll do everything I can to put this offer in the most favorable light possible.” They should jump at any chance to “earn” their money.

If you really want it and they won’t deal with you, then lesson learned by you. Unfortunately, the sellers wouldn’t have learned anything. In this market, I’d take a reasonable offer if I needed to sell.

No point in bidding against yourself with a moderate initial offer.