I'm no patio11, but I did follow (I think) a similar trajectory. I used my consulting gig to build a nest-egg that I invested in my own startup, which will hit $1.2MM in revenue this year. I wanted to augment his comments with a couple of things that I know worked for me.
> I know networking goes a long way toward such contacts, but it can't be just that.
For me, it was literally "just that". However, understand that "networking" is a vague term. For me, networking was more than just showing up at social events and being nice to everyone, although that certainly counts. For example, I had a reputation for showing up at my clients' offices any time there was cake (birthdays, etc). It became a kind of running joke with everyone, and always got lots of laughs. But I digress.
Networking is the subtle combination of being present and expressing your value to those who are interested. This does not mean shouting your pitch at everyone you meet. Rather, it means listening to what people say, thinking about the challenges they're facing, then offering your advice on how technology could help them.
> One thing I'm still struggling with is how to explain and justify the (otherwise normal but perceived as) high cost of web development to a crowd that's anything but tech savvy. How do you justify your consulting fee? "Everybody charges that" doesn't sit well with me...
Maybe I'm just being narcissistic here, but my very favorite piece of advice for people in the technology field is "stop selling technology". The person you're selling to isn't interested in buying technology. The world is full of companies selling technology, and the buyer you're targeting doesn't understand any of it. The most successful sales pitches I've been a part of (and continue to be part of) are couched entirely in the language that the buyer uses, not the language I use.
Take a second and internalize that.
The small business owner doesn't have the time to become an expert in technology. They might even think that they do. For example, I would occasionally have a customer ask me what technology we used to build our websites. Some customers would ask about specific technologies: "Do you use 'pee-aych-pee'?" I would always deflect those questions tactfully by explaining that the technology that drives a website are nuts-and-bolts, which we can figure out once we really understand the problem the customer needs to solve. I would say something like:
"As a geek, I'd love to talk to you about PHP, Ruby, and ASP.NET, but I think that might be getting ahead of ourselves. I like to approach technology problems from the other direction. All of those technologies are great, but they're a means to an end, not an end in themselves. Let's talk about what problems you need to solve, then figure out what technology fits best."
If the client doesn't light up when you say that, then you're probably talking to the wrong client. It's very difficult to work with pseudo-experts. They end up meddling too much in the technology side of the work.
Back to the bigger picture, I don't think you're "thinking too small", although you might be thinking of this from the wrong direction. The best way to convince people to do business with you is to sound like them. Use their language. Put a lot of effort in to understanding them (their role, their challenges, etc). Resist the urge to jump right in to technology. A deep understanding of clients' problems will save you, even when/if you make a bad technology decision. If you do these things, you'll never have to justify your price. That doesn't mean that everyone will want to do business with you, but it acts as a natural selector for the types of clients you want to do business with.