Thanks for the writeup, I'm glad there's some renewed interest in this.
I can't figure out what the difference is specifically, though, with what you've written up. The proposal in this thread already includes commitments to back links. The way I think of it is that each block contains a claim about how much cumulative work went into creating it. The proof process is basically a hypothesis test, for whether the actual work matches the claim. In fact it's a recursive hypothesis test, because if you follow the "up" links you quickly (O(log n)) arrive at a block that should divide the total cumulative work into two segments. Then you do the hypothesis test on each of these.

I'm currently trying to figure out how to phrase this as a formal security game, which should make it a little more clear how to evaluate whether either of our proposals actually achieves what it's supposed to.