My assumption, which I am perfectly willing to have challenged, is that these VC's would understand the industry and grasp pretty quickly the significance and value of what it is I'm trying to do. Then I would subtract from the list any VC's that backed what I consider a competitor, and approach the rest.
One possibility would be to simply find every law related website out there and try to figure out who backed them. Another possibility is to go to every VC website I can find and see if they give a sufficiently detailed list of their projects to see which ones were law related. Both of these approaches strike me as being extremely labor-intensive and time-consuming, not unlike going to the library and doing it by hand in a book. So I'm hoping and assuming that there is a better, faster way to do this, which would also be more comprehensive and less likely to miss out on firms than the aforementioned approaches. I'm hoping you know what that is and can tell me.
And if there is a book that is not online and does what I need, let me know and I will go to the library and get it. ;-)
Venture Capital Legal Research
Well, this doesn't completely answer your question, but have a look at AngelList.
AngelList is a very comprehensive list of angel investors. Searching for the term "Legal " results in 8 investors that are specifically interested in that category, and a ton more that are indirectly interested.
Check out http://www.crunchbase.com/ It has detailed information on a lot of startups and businesses. You can do some recon on popular law firm sites such as:
http://www.crunchbase.com/company/avvo Some popular sites like FindLaw are however not VC backed, but are still in Crunchbase and have information about them.
Who are your competitors? That should be a short list of no more than 10 companies. Who is baking them?
If you have no competitors, stop: something is wrong.
If none of your competitors are VC funded, that's also a very bad sign.
It's unlikely that we can help you beyond such basic advice. You could go on TheFunded or AngelList and search for various keywords to see what comes up.