I am astonished that Fair Trading is apparently colluding with your neighbour to get you to pay to rectify their mistake in laying inadequately insulated floorboards.
And while I am all in favour of mediated solutions, the hardball approach is quite simple – no floorboard, no problem, therefore the upstairs owner should be re-laying the carpet entirely at their expense.
I get a sense from what you are saying that this neighbour is deliberately delaying a decision to avoid having to do anything.
However, I can see that you might want to spend money on fixing the problem rather than, say, legal fees, so here’s what you want:
Fully insulated carpet professionally laid with “gold standard” insulation underneath.
A signed agreement from him, lodged with the Owners Corp, that he accepts that timber flooring is inadequate and that he will never remove the carpet from his apartment unless it is to replace it with carpet insulated to a similar standard.
A rider added to his title deeds saying that the carpet may not be removed by future purchasers.
I added the last two elements because this person is perfectly capable of ripping up the carpet again just before they sell the unit, with the deal done and dusted before you can even register a complaint. Then you would be in a whole other mess with the new owner.
Frankly, if it were me I would just stop all negotiations now and roll on to an adjudication at the CTTT and then, if need be, a hearing. If the CTTT does one of its customary logic flips, you can appeal to your District Court.
But if you are reluctant to go down that road, then go in with a once and final offer which has a limited time and has very clear parameters on when the work will be done.
If they show any reluctance, tell them you will run the case through the CTTT.
Assuming your by-laws include the standard item about not disturbing the peaceful enjoyment of another lot, you should, if you prepare your case properly, have every chance of success.
And you really should think about talking to a lawyer, just to find out if running the case is going to cost you less than re-carpeting the upstairs flat.