Mentioning your citizenship might help, certain countries look for certain groups (e.g. they have a satellite team in ___ where you speak the language, bonus!).
I went to university in the UK, exchange programme in Santa Barbara. I did summer jobs in LA, Switzerland, Taipei, Vancouver, Auckland, Korea, China, and India. I decided I like NZ and Canada the most. I need 3 years prior continuous relevant work experience to get the visa. So I came back to Taiwan to do that. Now I have the academic and work qualifications needed.
I really want to stay and settle down. I don't have a "home" to go back to. If I live with my parents, I'm unable to marry or have kids. Those kids would be stateless because I'm a citizen by descent and can't pass on citizenship. NZ's Skilled Migrant Category can get me Permanent Resident status in 2 years (the fastest). That's my plan, but I need a job to help me do that.
Why wouldn't your kids would get your wife's citizenship in most countries? Also your (future?) wife's country probably has marriage visas and what not.
I know a mother and son from church here. She went to NYC, met a Chinese man, got married, had a kid. Moved to Canada. He went on a business trip and cheated, they divorced. Without him, she lost her Canadian residency. The kid had 4 passports (US, Canada, China, Taiwan - dual citizenship is allowed under 18) but he couldn't live with his mum unless they moved to Taiwan.
Aged 15, all his education in English, suddenly expected to study at a local Taiwanese school. Last I knew they were trying to move to Germany.
Taiwanese (and Canadian) permanent residency aren't permanent, because if I leave for more than a couple of years I lose it. NZ PR is permanent. (Or 4 years to Canadian citizenship).
The other two options are more hopeful - Canada will allow me a second working holiday (my first was before the rules changed in 2012), and I didn't work in Australia before. But the Aussie visa only lets me work for one employer for 6 months max. NZ needs 3 years continuous relevant work experience, and I really don't want to break the "continuous" part I have now.
You were already successful to find skilled job before, so you will be able to get it again. And being physically here with open work permit makes things much easier.
Then you can apply for Young Professional which is very little hassle for your employer and you will get 2nd year easily.
And during this 2 years you would apply for Express Entry as soon as you are eligible. You apply for FSW for which you should be eligible already or for CEC when you have 1 year experience in Canada. If you don't have enough points for EE then there are other programs like PNP.
It would be really bad luck if you couldn't get, or be in the process of getting permanent residency during that time. When you have job in IT, it's quite straightforward to get PR.
Also, when looking for job, never mention word "sponsoring". When recruiter asks you about your visa you will say that you have WH for a year, already lined up YP for 2nd year and applying for PR as soon you are employed. Visas are not a problem here.