Of course you will not find the tool you want as it doesn't exist. There is no such term as accuracy in Google. It is all about geo location. When you live in USA you will see different results than if you live in India, Japan or whatever. The same with the manual checking - the serps you see are accurate for you but not for me. So the tools you consider as inaccurate are just hosted in places different than the one you live in.
This is not really the problem, as most of these tools allow you to select country specific search engines. Really the difficulty comes with being able to parse Google results efficiently. Occasionally you'll get things like google maps appearing at the top or indented listings, these can all screw up the parser's accuracy.
I have to disagree. Every single SERP will contain the same html for each result; the same class, a href structure, etc. It's extremely easy in PHP for example to obtain these links. Google, however, has multiple datacenters which have slightly, sometimes drastically, different results from each other. My site may use a different datacenter, but you can see if it works for you.