On one hand, I wonder if a gradual transition would work. Spend enough time over the years mirroring your conscious patterns onto a computational substrate, and they might get used to the lay of the land, the loss of old senses and the appearance of new ones. There might not be an ultimate "stepping in", but something like you might be able to outlive you, on a substrate that it feels happy and comfortable on.

On the other hand, the idea of "simulating your consciousness" raises questions beyond just cognition or personality. A mechanistically perfect simulation of your brain might not be conscious at all. Spooky stuff.