If I permanently moved outside of Canada in 2017, can I claim moving expenses? Or must I be a deemed resident for the entire 2017 to be eligible to claim?

Self-employed

Yes, you need to be a factual or deemed resident of Canada to be able to claim your moving expenses: https://www.canada.ca/en/revenue-agency/services/tax/individuals/topics/about-your-tax-return/tax-re...