ICT or LIMA

Hello all. I'm trying to immigrate to Canada with my family. (And I'd like to move as soon as possible)

From what I can tell; I can move there immediately if I have a work permit and then after a year apply for express entry to improve my score. (Please correct if I'm mistaken)

Previously, I was working for a US company remotely. They were recently bought out and I didn't continue employment when that happened in December. Now they would like to rehire me. They have entities in both the US and Canada and know I would like to move to Canada. Help me help them. Is the best route for them to hire me through Canada with a LIMA or hire me through the US and then file an ICT?

For the ICT I noticed you have to work for a company for a year first. Would this mean we can't go this route since I was off their books since December? Or that it's technically a new company since I was working for the one that was bought out?

What's the easiest, fastest solution? Thank you all for your time.