I don't recommend the installation of any 'new' siding over an existing one because of the relative unevenness that can occur. Plus, you may void any type of warranty. In your case, you don't want to install stucco over the shingles because 1) The shingles may not be adequately anchored to the wall sheathing, 2) the old siding can 'move' under the stucco, 3) you may void the warranty on a 'good day', and 4) unevenness.
I can't say what it would cost to install. Your best bet is to have 3 contractors come it and give you SEPARATE estimates for demolition AND installation. THen, you ctc each of them and ask 'why is one more, or less, expensive than the other.' See what one is including, or not including in the price. At the same time, by the time you've spoken to the 3rd bidder, you're a much more educated consumer! You may be able to do the demolition yourselves since the shingles are considered non-friable. And they generally contain less than 1% asbestos. (If you decide to go this route, e-mail me directly later on w/any questions or Post up on the forum.)
I've included a few links that talk about the installation of new siding with regards to asbestos shingles, among others. Although you might find that they don't, 100%, apply to your specific question, there's good info nonetheless. So do read through them and 'absorbe'. My best to ya and hope this helps.