Your low ball negotiation idea didn't work at all but still you say don't use an agent.... 
No, we low balled it with the very same agent that brokered my current home. Only difference is that at the time there wasn't a $3,000,000 home on the other side of the deal, so he was happy-uppity about getting some offer traction. I didn't know it at the time but... we were getting played into desperation mode.
Bottom line is that a buyer should always low ball a house that does not meet ALL of their demands. It's called negotiating. If you don't, you have plenty of time (30 years) to bitch and moan about the lack of this and that.