I tend to agree with everything you said as I estimate projects on the design side. It is much harder to estimate when there is no design (as I do the designing). Having a quantifiable design make estimating much easier as opposed to a client that "thinks they know" what they want. If you do not have something on paper, put it on paper and make sure it agreed upon.
From there I tend to take two approaches - piece by piece and as a whole, along with some 'gut feel'. Example would be - a box of cookies should cost $1 for a box of ten(the whole/gut feel), but then I would figure a single cookie takes 1/2 oz of this, tablespoon of that, and 1 minute of mixing, 2 minutes of baking, electricity.....times 10 (piece by piece). If the two come out to about a dollar I run with it. If not, it is back to "what have I missed?" or "what have I over assumed?" Sometimes if they do not agree I make sure I document exactly what I am giving and not.
Documenting what you are going to give and not give is how some contractors give "less of a product" such as "I will provide 5 chocolate chips per cookie" where you will provide 10/cookie.
My nickles worth.
PS do not forget your overhead - this computer I am using was not free!