Well, if you rent a U-Haul, on their website you will find e-Movers, they will come Upload in USA and Unload in Canada. I wanted to go that way as well, however I have family and I cannot take everyone in the Cabin with car seats.
I have used e-movers help for loading and unloading and they are amazing, two people will come and move everything while you sit and drink Coffee.
If you really want to use the moving company, Atlas moving is the best as per my friends experience. You can reserve them Online and the consultant will explain you everything, you can buy insurance for your electronics etc. as well, but of course, it is pricier than U-Haul ~ your choice.