I'm a contractor, and sometimes negotiation is ok. Usually this is done by just getting different bids. But you have to be clear about what work is going to be done and for how much. Additional work costs extra, so be careful not to negotiate for a desired price point when you actually expect more expensive work. A written set of specifications that the bids should be based on is a good idea. This way, everyone you talk to is bidding the same job and you are comparing apples to apples. Get bids in writing. Check on insurance and bonding.
Usually, a negotiation on contracted work as you describe will consist of a contractor's bid, a counter bid or similar response, and either no response, the same price, or a reduced price with some sort of compromise on work or materials that should be explained. For example, a recent bid I made for a door replacement was counter bid to be under my cost and without tax. My response was that I could do it for their price but with a different, cheaper door. They chose the higher quality door.
Your second bid of $1K represents under 2 days of labor for contractors in my area. Then there's quality materials, custom milling, demo and install, perhaps paint as well?
I would suggest looking for someone who specializes in wood windows. If you can preserve the original windows, they're often better than new, especially vinyl. Get references and referrals from neighbors who have had similar work done.
