Just wanted to chime in here because I spoke with someone at the border about this very thing..
Originally we were going to rent a U-Haul and planned to unload directly into the place we're renting in Toronto. The lady I spoke with said that we were NOT allowed to even return the truck, even with the option of contact-less drop off. She said I could have a friend or family member return the truck for us but that under no circumstance could we go anywhere outside our new home.
Have you considered using U-Boxes instead? It's a bit costly but you have the option of them moving and storing your stuff for you, all you have to do is load them. For NY to Toronto it was going to be roughly $3500 USD for two-three boxes. We used this option several years ago moving from Toronto to Dallas and it was about $5000 USD and took about a week to get our things.
This time around we ended up going with a moving company and because they're considered 'essential', that helps alleviate the stress of having to quarantine since they can still come into our home to unload our furniture. However we have to get a family member to clear our goods on our behalf since we can't go to the customs office. Annoying but, it is what it is. This option ended up being around $4000 USD.
I hope that helps! Let me know if you have any other questions.
