Canadian citizen - live in the US (last stage of green card) and work remotely for Canadian arm of a US company?

This is a bit of a complicated question.

 

I am a Canadian citizen, living in the US as part of my adjustment of status towards obtaining a green card. I used to have employment authorization to work in the US which expired every year and I had to renew it to continue working. This was a standard process but currently due to Covid delays the renewal could possibly take a long time and I am unable to work in the US (but can continue living here). If I leave the country my green card application will be cancelled. 

 

So I am looking at a scenario wherein I get hired by a US company with operations in Canada and ask them to employ me in their Canadian division with local salary which would make it a Canadian entity but with the possibility of working 'remotely from the US' since I am already residing here. 

 

Would this be feasible and logically make any sense from the tax perspective? I am aware that any source income earned abroad has to reported to IRS. But not sure if that affects my stay and green card application here in the US.