Does it have to be through networking?
The reason I ask is that generally only the really small companies can afford to only hire through social networks. Most of the ones with more than a couple of dozen staff need to fall back on recruiters and this gives you an alternate approach.
I took this approach at my last job change, I'd only been in the city (Sydney) a year or so and was working for a largish place that I absolutely loathed. With few local contacts I took the recruiting approach, after literally dozens of phone interviews and a fair number of face to face ones I finally found the right place. And I knew without a doubt that it was the right place, which is a sensation I'd never had before.
What I can tell you about the recruiting experience is that it sucks, but with sufficient time and effort it can produce results.
The keys to success are as follows:
This will take time, so you will need to stay in your current job until you find a new one.
Talk to as many recruiters as possible, they will all say that they are out there looking for the perfect job for you, they are lying. They have a bunch of client companies that they recruit for they will show them your CV then put it in a filing cabinet.
Keep a list of everyone you talk to and every company they put your CV into, trust me this will make life lots easier as things progress.
Where cover letters are needed make customized ones, the best way to do this en mass is to have a couple of dozen prepared chunks that you mix and match to suit each position you need a letter for. You can distill these chunks from the first few letters which you will just have to custom write from scratch.
Finally and most important, at interviews you are interviewing them as much as they are interviewing you, make sure you ask about hours, overtime, dress codes, the tools they use, the hardware you will get etc. Remember also that the interview is an indicator of the sort of people they hire, if the interview is dead easy then it means most of the existing employees are probably retards.