Unrelated to your question, but have you come across the Employment Gold Card yet? If you qualify, it could open up a wider range of job opportunities to you, since employers would no longer need to sponsor your visa. There’s a lot of info over at "Employment gold card" for some foreigners , but give it a google or check out my little write up.
One of the holders, @irish91 might be able to share some of his story about applying for software developer jobs before migrating & if he found cover letters required.