In all respect, but from what I read it seems you still haven't understood my proposal. You are talking about "last minutes/seconds of a burn period" but what I propose is a sliding window, so there is no end of any burning period!
Furthermore, in your argument you somehow make the assumption that the free market to decide if burning is profitable will not work. If your argument would be valid, then the whole bitcoin mining would make no sense, because free market decides if your energy costs are worth to mine bitcoins. So the decision to mine Bitcoins or not to mine Bitcoins depends obviously on the exchange rates in the following loop:
BTC(exchanged) <-> USD -> proof-of-work-energy-cost -> BTC(mined)
A miner can calculate his rewards and the free market will decide if it is more profitable to go the route via exchanges or to mine.
My proposed system actually completely rebuilds this free market reward system:
NEX(exchanged) <-> BTC -> proof-of-burn-btc-cost -> NEX(mined)
I agree on the need to burn something. If there is no cost to a good, then there is no floor on the price.
What is extremely interesting about this proof of burn is that it is quite egalitarian as compared to the centralized mining that we have today for BTC. Anyone can participate to burn their BTC to mine NEX. There is no extra advantage that you happened to be lucky enough to acquire a pre-order ASIC mining machine.