Hi Ricardo,
You are 100% correct. I made a mistake. Thanks for catching it! I've made the correction and added some more. Also tagged you for pointing it out.
What I wrote is clearly wrong: “You are seeing the ship as it was 1 light-minute ago.” It should have been: “You are seeing the ship as it was 1 minute ago when it was 1 light-minute away.”
Even this is an approximation and can be improved further since the light from the ship could have traveled more than 1 light-minute and thus from greater than 1 minute ago due to: (1) Non-zero amount of space expansion during that minute and (2) if there were mass somewhere near the path causing bending of spacetime, and thus forcing light to take a longer path and taking longer than 1 minute.
Kevin