Importing a Mopar from Canada to The USA
Importing a Vehicle from Canada | ezbordercrossing
Perhaps you have already looked at EPA and DOT compliance which is more reporting than anything else if the car is over 25 years old. You can complete the forms. Yes a customs broker can get the vehicle across for you.
As to the actual deal, in British Columbia there is a form, APV9T, that is completed to document the sale of the car. The seller will hand over the BC registration at the time of purchase and the sale amount for tax calculation is documented. In your case You would not pay the tax because you are not going to register the car here. Info is all online for this province.
I think It would be best for all docs (Bill of Sale, Transfer form APV9T, etc) to be in the same name if you are going to cross over. If it is someone else other than the new owner that person might have to provide a brief explanation to CPB. As per above you would have already notified CPB you are coming and if tax is payable they get you there.
Happens all the time so all of the info is online. Border towns would likely have a storage lot/pick up point for auto transport to all points in the US.
I am 5 mins from the US/Canada border in BC.