According to my company, this arrangement has - quote - "severe tax implications" not just for you, but also your company, so make sure they are onboard with the arrangement.

In the most basic terms, the problem is that some tax is withheld (i.e. paid to the tax agency by your employer in advance on your behalf), and that must be done in the appropriate country.

IANAL, but I recommend that you keep track of how many days you were in the US each month, and how many of those days were for work. It's likely that an accountant or tax professional will ask you for that information to support your claim of tax residency in Canada.