As you've been in you current job for a fairly long time, it might be an idea to check if the company has an office in Calgary. If they do, you could look into the opportunity of getting an inter-company transfer. In such cases the company will take care of your visa and that will be a lot less stressful.
If you could get the skilled workers permit, it would make getting a job much easier. But you can also approach companies directly. Calgary is one the fastest growing economies in Canada and there are lots of opportunities over there, especially for engineers and your past experience will also work in your favour. Have a look at the Working in Calgary and Work Permits for Canada section for more information.