They will either have to set up a US payroll for you, or make you a contractor.
The people you should have been talking to were your employer, not CRA.
This was something to negociate with them, not with Govt.
You might be in for a nasty surprise now, as many companies don't like to have to set up a foreign payroll for one employee, and they may let you go or make you a contractor with no benefits (which is fine -- Cdn benefits don't count for much in US).
You will now have to pay US social security and medicare (either as an employee of this now-US company) or as self-employed in US on this income. You will aslo have to make sure that you send at least quarterly
taxes to IRS and state on your income.
And your Cdn company may have to withhold some taxes as well, since you are non-resident.