I applied for my first job, back in the days of sponsorship, tried and failed numerous times.
After putting myself through the training, qualifying, I did pretty much exactly what you mentioned, to get little response. I did not only target airlines (I think this would be the wrong attitude, to only target airlines). The CV went off to every operator I knew of. One thing you have to realise is, every man and is dog with the same credentials is doing the same thing. I remember a few years ago, myself a couple of friends went down to Europen when they were recruiting and took our CV's personally, thinking it may make a difference if we showed our faces, only to be greeted by the receptionist, to say, oh thanks, you can put it over there with the rest. The rest just happened to be a pile around 4 feet tall of CV's
.
There are numerous ways of getting your first job. From my own experience, unless you are
very lucky, it will prove a difficult task. In order to maximise your chances, you have to think of ways to enhance your experience and skill. This can be in the form of towing gliders, instructing, doing survey work etc. It also shows you are determined and are not just stting back and waiting for the job to come to you. Another key point is to network with people. Having someone to have a word in the right ear, or place your CV on the right desk, has tremendous strength. But this is not something that will just happen overnight, you have to know the right people, and have their respect.
I wish you all the best, when you get your first break it's worth all the hard work believe me.