Don't lie. Your domicile evidence goes with the affidavits of support. Unless and until NVC accepts that evidence, you will not even be in the queue for an interview in Montreal. Yes, it is an advantage to go ahead and move ahead of your husband. The checking into schools was not about your children's education. It's about the domicile issue. Homeschooling is fine but it will not help with the domicile issue. You can kind of pseudo move also, in that you can go ahead and get your local driver license, bank account etc. for what (to you) is a temporary stay preparatory to the permanent move. Firm evidence of your husband's continued employment with the same company's US branch etc. is a key issue do firmly document.
A receipt for moving expenses for a portion of your household items can also be used if practical for you.