Canadian citizen living in USA, Best way to set up a Canadian company for a contract with a Canadian client?

Hi folks, I’m a Canadian citizen living in USA with a green card, running a U.S. based LLC. I have an upcoming contract with a company in Canada, and I want to keep it clean on the Canadian side. I’m considering setting up a corporation in Canada and having that company sign the contract.

Then, the corp would subcontract the work to my U.S. LLC where I will do the work.

Anyone done something similar?

Should I set up a corporation or an LLC (does Canada even support LLCs properly?)

How are intercompany payments handled?

Any tax pitfalls to watch out for on either side of the border?

Is this a smart way to keep things clean for the client and still run most of my operations in the U.S.?

Appreciate any advice or experience!