Does this sound right to you?
It is right.
Normally, you'd say "who should simply leave the Internet" But this time the clause is the object to the previous chunk, the clause that tells who does what to whom, "I believe whom" That is the previous chunk and the main clause so you stick with whom even though that noun is the subject of it's own continuing clause, this time it's an object clause.
I believe whom/who should leave the internet.
And oddly, the same thing happens in hieroglyphics and the same thing happens in ASL. The noun as object has its own form and keeps its form as subject of its own clause. In hieroglyphs all of the "it" "you" "he" "she" "them" all those things change, and stay that way as the next chunk continues. In sign the same thing happens. When subject noun A does something to object noun B then B is positioned where A left off and whatever B does after that starts where A left it. Out there in left field perhaps. So it's changed. You do not revert to textbook sign for B because A did something to it and your story continues.