Might the results of your survey be useful to LPs, the folks who give money to the VCs?  These are often government employed pension fund mangers, or private endowment mangers with a natural interest in asking questions about VCs.  If you can partner with such an institution, the VC will become your lap dog overnight.  

You might pursue this on Linkedin, especially with some of their groups. Your survey instrument could be linked to your message or post on Linkedin so that those interested could go to the survey. It would not be random, but it would reach hundreds of thousands of potential responders.

I think you try to look at various modus operandi of VCs, then you can choose some models you interested in,,,based on my understanding, there are many approaches in Islamic finance as well such profit and loss sharing methods, and Mudaraba contract ( one party manage the business while another party supply the capital),,, then from that you can develop your research.. 

Good counsel. Thank you.

Hope this is not coming too late. If you've got time on your hand, try PE and VC associations and groups, and be persistent with them. Attend a PE/VC local conference and get them to commit themselves, just a few. You can then build on that track.

Surveymonkey.com has an audience of over 30 million and, for a fee, can locate sand sample this population. However, this sample is considered an "elite" sample and the cost will be much higher. You might want to contact them just to get some quotes.

Lists are easy to come by. Response is an issue. VCs are known for ignoring cold intros. Warm introductions work best. Look for alumni with contacts for example.