Isn't this one of the beauties of the internet? Once it's out there, there's no deleting it.

I don't think it's morally wrong to keep the archive. As most people do for famous accounts such as politicians.

I'm not sure about the technical solution, I do like the blockquote approach. Better than a simple screenshot. I don't usually embed tweets in my posts but if I did I'd probably copy and paste the content into a blockquote and a link back to the original.

Have a great day!