Here's what I learned yesterday by doing more research on my own after receiving the estimate for a B-vent chimney:
I found out that there is a difference between a "chimney" and a "vent". The first link below describes that, although it is dated 1991.
I also found out that the height requirements vary with chimneys and vents depending on the type of construction and the type of boiler, furnace, etc. that is being vented into the chimney/vent. The second and third links below describe that.
Basically, for any masonry chimney, or a Type L vent, that is being used on an oil-fired, coal, etc. type of boiler, the height requirements are that it must go up at least two feet higher than any point where the roof is within 10 feet horizontally from the chimney/vent.
BUT, for a Type B vent, which is only for gas-fired boilers etc. (which is what we have), the height only needs to go up about 2, 3, or 4 feet above the actual roof line where it comes through the roof -- depending on the slope of the roof. After reading that, while driving around, I see lots of metal B-vent "chimneys" that only come up two or 3 feet off of a sloping roof, even when they are on the low side of the roof. I found that to be VERY interesting!
Here are the 3 links:
http://www.homeinspector.org/resources/journals/Chimneys-and-Vents.pdf
http://www2.iccsafe.org/states/newjersey/NJ_Residential/PDFs/NJ_Res_Chapter24.pdf
http://www2.iccsafe.org/states/newjersey/NJ_Residential/PDFs/NJ_Res_Chapter18.pdf
One thing I figured out after seeing a guy who was maybe 5' 8" or 5' 9" tall from the last chimney company actually walk up on the roof and stand on the roof itself next to the chimney and reach up to almost the top, is that it would be easy for us to take down the existing chimney. At most, maybe a roof jack ledge on the high side of the roof to stand on and reach right up to the top and take down the chimney piece by piece, brick, by brick. They are so loose they will come off by hand or maybe with a very light tap or pry bar. Or, I have a large Werner "A-frame"(?)-type ladder that we could place on the porch roof next to the chimney and reach the top of the chimney from there without even getting up on the top roof where the chimney is located. So, the cost of the demo will be almost nothing. Then, all that will be left is to drop a metal B-vent down in each flue, connect it up at the bottom, do the right cap routine at the top, and it's done -- no scaffolding, etc. will be needed.