So, if someone generates an image on their laptop using solar power, using locally run hardware, is it still inherently wrong?

It is not inherently wrong. In your use case I would have less issue with it.

What is the advantage to artisinally fashioning a meme with the same message, when memes are inherently a low-effort, mass-produced form of social expression?

I do not mean to be rude, but I struggle to see how I did not answer this with the "the medium is part of the message" part.