I'm not a builder/buildee, so I have no advice on the construction, but what I do have a lot of experience with is estimating jobs. Now, the jobs I estimate are for automotive repair, which is a little more standardized. However fair and honest I try to be, if someone tells me (or their attitude makes me suspect) that they will be shopping around, I double-check to make sure my estimate is accurate and clear.
Why? Because I know that another shop might see my quote, and I don't want to give them ammunition to bash me with the customer. If I quote a job at $400 and another shop says they can do it for $250, not only do I lose the job, I lose some of my hard-earned reputation.
When I was looking for a price on the roof of my garage, I got 4 quotes. One was a pro roofing company that does business with my work...they were the "middle of the road" (written) quote, all their math jibed. I had another pro roofing company that just gave me a quote over the phone for almost the same price, but I didn't accept that based on the fact that they never even looked at it, measured it, or anything. That tells me that they feel they have enough profit margin to overcome any issues, or feel comfortable coming back to me and asking for more.
The point of this block of text is actually the low bid - a longtime customer of the shop I work at who is always coming in and bullshitting/showing off pictures of his work. He came out and looked at it, bullshitted with me for awhile, and then gave me a written quote a few days later. Told me if I paid his cost on materials he'd do it for $700 labor including the dumpster. If I was a trusting guy, I'd have taken the bid then and there (it was $1400 cheaper!). I think that is what his business is based on. But I read the quote and realized he was billing me for enough material to roof multiple garages. 300' of drip edge? 16 sq of shingles? 24 tubes of solar seal? Its a 24x24 for shits sake.
My boss hired him for a remodel of a 1/2 bath.....and 2 months later it is almost done and only $2000 over budget!
I guess my point is this: compare apples to apples, get references, and if a "professional" doesn't want to act like it, then he doesn't need your money.