A substantially different variant is to pay for every share at most once. If, when going backwards in the list of shares, we encounter some that were already paid, we skip them and move on to older shares. X needs to be less than 1 to make sure that eventually we will have enough unpaid shares to draw on. I'm not sure what's the correct way to handle difficulty changes with this variant.
In effect, like a pool charging a 1% fee but paying that fee to past-due shares instead of it going to the operator?
Not really. If for example X=0.5 then still normally a block will be paid out 100% to recent miners - each share will be paid twice the PPS rate. But in lucky times when there aren't enough unpaid shares, past miners can be paid.
Payment always starts at the last share and continuously moves backward as much as possible, skipping any already paid shares.