Have you considered working with any third-party recruiters? It seems that going through one is the only way to get the attention of most companies, these days. I would advise not taking the lack of responses personally, because cold applications are, generally coldly, disposed of (a human never passes judgement on them).

FWIW, I found my last two jobs through third party recruiters, and still count them as friends. It's an industry with an oddly-poor reputation, but there are some real gems of people to be found in it.