Ian:
VC's and PE firms do engage people in the role you're describing. And, they are a pretty 'clubby' group, getting access and 'breaking-in' is challenging...will take time to make happen. You've got to demonstrate your 'chops' for sure.
1. Use Founder Dating network to meet a couple of VC's out here and see if you can get a discussion going with them.
2. Look for a chapter of Association for Corporate Growth (ACG) in your area - it's a good networking opportunity to meet people who can help you meet people.
3. Get your elevator pitch really down - and I'd suggest you dump any language that talks about being bored...survival...etc. Create a positive 10-15 second intro for yourself that emphasizes what you are 'running to' not running away from, which is what you sound like in the original post - VC's and PE people are generally quite successful and want to associate with people who are equally successful - you want to create an 'eyes level relationship.
4. Have a good 'profile' document - you may need a several - one that is more 'traditional resume' formatted; one that is 'web bio' formatted to tell your story on paper succintly
5. As someone else suggested - connect with a business incubator in the area - often they are strapped for budget and it's a place where you can 'earn some stripes' in this area by contributing your time / energy there and build a profile for yourself that can extend ultimately to VC / PE people.
Again, give it time...this is NOT going to happen overnight, despite what all the media hype says about rapid rises to success...Remember that Rovio had more than 50 failed games over years before Angry Birds 'hit big;.
One book I recommend to a lot of people in similar positions is "Get Clients Now" - it's a good primer on setting up a process for yourself and sticking to it over time.
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