I have to say I'm getting utterly confused here so let me just clarify a few things:
As a Canadian who owns a CCPC, you MUST have your tax home in Canada, Canadian law requires it. If you're working in the US pretty much indefinitely, there is no point in having a CCPC because it just causes you problems and you should probably dissolve it (which may expose you to departure tax but face the reality!)
You can if you want file as a non-resident in the US, but the IRS will start asking questions if you do it for years on end. You file a 1040NR and an 8833 in the US if you're there for more than 183 days, 8840 if it's less than that. This only makes sense for a long period if you have a CCPC or for some other reason you must keep your tax home in Canada e.g. exposure to lots of departure tax. Eventually if you're filing a 1040NR with a US address on it every year, the IRS will write you a letter asking for proof of residential ties abroad.
You can if you want have a CCPC in Canada, but work as a self-employed person or directly employed person on an entirely separate payroll in the US and this is advisable to avoid the CCPC having to file a ton of paperwork in the US and having a US payroll.
The question about "working on a 1099" is a bit disingenuous, because if you're a non-resident alien there is no 1099, it's not a relevant form for NRAs. Payment is made on 1042-S but this is optional because there is no NRA tax so in fact there is nothing, all you have to do is prove your status to your client which is done on Form 8233 and they keep that in a filing cabinet somewhere in case they're ever audited. If you're directly employed you state on the W-4 that you are an NRA (find the instructions that tell you to do this, I dare you, they are fantastically obscure) and they just give you a W-2, it's as simple as that.
BUT really the better option if you're doing TN-1 in the US for a long time is to simply scrap all the NRA stuff, close down your CCPC because you clearly don't live in Canada and do your
taxes like any other American does.
I was advised by the IRS many years ago that it is unwise to file as a non-resident alien self-employed person because it's the rarest filing category (hint, hint, nudge, nudge, audit, audit), so basically not a good idea to either have a CCPC and set up a US payroll for it because of the paperwork and not a good idea to have a CCPC and file as a non-resident alien self-employed person in an attempt to avoid that paperwork - get rid of the CCPC and file as a US resident.
Okay, that's the NRA bit covered.
There's another issue which goes to whether you can be self-employed on TN-1. I've had this discussion in depth with the IRS legal dept. if you can believe it and although the IRS doesn't care if you file that way, there are various international treaties involved (tax treaty, NAFTA) and legally it's very confusing, which is why I quote the bit from the CBP manual which is slightly less confusing. Essentially your sponsor must be arm's length from you, you cannot in any way control them or their company.
Assuming you're okay with what CBP may think when they ask you if you're self-employed then from a tax standpoint you can do what agnelson suggests - get 1099s once you are a US tax resident which does make sense in the example he gave, a guy with 14 TN-1s because it's impractical to be on 14 payrolls.
But don't be a naive Canadian and meekly accept a 1099 when this person is your only client - employers do it in the US to offload social security matching on to you and then you have to do all the self-employment stuff as well. If you're working principally for one company then really you should be on their payroll and getting a W-2.
This is advice the IRS gives to Americans employed in the US, let alone Canadians.
Steve.