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I assume that the third instruction applies to the third grid (i.e. the two-puzzle one) and that I am to replace letters in it with this latest Greek letter in the positions they appear in the very first grid. A preliminary check along those lines does not look very promising, but is it correct?

No, the third instruction should be read as a two-parter: one word followed by three words. That first word applies to the whole grid. Once you've done that, follow the instruction from the last three words and compare what you have against the description of the final grid in the preamble. You're nearly there!

Thanks Twit. I believe I have now finished this astonishing puzzle. After all the help I have received from you, Candledave and Mooncow I had better not submit, but it is a great feeling to have finished it. Thanks again all.

Well done - great perseverence!

Now that the submission deadline is past, I don't know whether it would be considered acceptable for someone to provide a walk through of the endgame for those of us who gave up with it after getting intensely frustrated at the first hurdle?

I can give it a go from memory The whole theme was puzzles from the Saturday Review section of the Times and you would probably have identified the objects as Polygons which is a puzzle in the Saturday Review

The message was something like “nine letter ones round mus. Chi starts zeta ends”

So you had to identify 9 letter polygons around the 9 Ms preprinted in the grid and identify words from those polygons of the right lengths that started with the letter in the X cell (chi) and ended with the letter in the Z cell (zeta)

That gave the message “Erase all, obfuscate eta (the H cells), sort out codeword, use beta”

You then solved the codeword and read off the entries that started in a B cell to give a message “Erase all but Tau entries; solve letter sudokus; use kappa”.

You then had two side by side sudokus to solve and the K cells gave a message to erase everything and enter original nus - ie the letters that were in the N cells in the original grid which gave an appropriate quote in Latin adapted from Wren’s famous St Paul’s quote

Thanks candledave, much appreciated, still makes next to no sense, probably not helped by having no idea what the polygons are in the SR, but I'll try to work through it.

Where do the definitions that were excluded from the original clues fit in?

The definitions led to the length of the 9 word instructions

For example FONDLY in one of the early clues defined the adjusted entry DEARLY. In DEARLY, the L had survived and L is in fifth position in FONDLY so the length of the first word in the instructions is 5

SH, Google "polygon puzzle". One of our Sydney papers has the equivalent, always of nine letters and in the required format for this puzzle. It's called Target Time here.

The first part of the endgame, getting the nine words, was actually the part I found trickiest. The rest of it then was hard work, a long haul, but unfolded fairly steadily. Warning: this comment is spoiler-heavy, so don't read if you don't want that!

When you have a full grid, with two letters fighting for nine squares, one checked, the endgame starts. Some of the letter pairs resolve themselves, as only one gives a real word, but several of them could go either way, included the checked square. Using the "nine of the extras define an altered entry" resolves these, because in each case the word made by dropping one of the letters lines up with one of those definitions while the other does not.

The definitions I found from the extra words were
'Fondly' defines DEAR(L)Y -> 5
'Cistaceae maybe' defines BUSHE(S) -> 3
'went posthaste' defines (H)ARED -> 9
'chine' defines L(I)N -> 3
'browbeating' defines CO(W)ING -> 4
'of use' defines (U)TILE -> 3
'rufescent fruit' defines BIFFI(N) -> 8
'cage' defines (G)RATE -> 3
'egos in Caledonia' defines SEL(S) -> 4

The word lengths are thus 5,3,9,3,4,3,8,3,4 and the omitted letters are GLPNOLYOS, which can form POLYGONS. The other extra phrase, which we are told is the home of ALL the thematic objects, is "Saturday review". This is why I remarked at @146 that while having a Saturday Review to hand is not essential, having a general idea of what appears in it and what the rules of them are does help. Google is your friend if you're not familiar with it: a search for POLYGONS and "Saturday review" is quite helpful, especially if you add "The Times" into the mix -- even the AI overview start to work out what it's about at this point!

The corrections spell "nine letter ones round MUs. CHI starts, ZETA ends". We are looking for nine-letter polygon puzzles around MUs, and we need to find words of the relevant lengths starting at a CHI and ending at a ZETA. Capital MU, CHI, ZETA are "M", "X", "Z", so the preprinted letters do it all now. There are nine preprinted "M"s, and exactly one "X" and one "Z" adjacent to each "M". In a polygon puzzle, you can only use each letter once, and you must use the central letter, so together with the lengths it is fairly clear that the words that are required from each of the nine polygons are ERASE, ALL, OBFUSCATE, ETA, SORT, OUT, CODEWORD, USE, BETA. This tells us to "erase all" (start with a new grid), "obfuscate ETA" (a capital ETA is "H", so we shade in all the squares whose preprinted letters include H), "sort out codeword" (we now use the preprinted numbers and solve as a "Codeword", which is another puzzle that appears in the Saturday Review), and when solved we "use BETAs" (a capital BETA is "B", and we notice that each B appears at the start of one of the words in our codeword, to get our next instruction). By now the vibe is probably becoming clear, and there are more hints as to how to work through the next parts across posts 140-160, but I'll add a few notes.

NB if you actually "erase all" as the first instruction suggests, you'll be hopping mad when you reach the third instruction, which asks you to reinstate some of that original gridfill. I hope no one was rash enough to really rub everything out...! I print out the Listeners, and I used four separate printouts, for the original gridfill, the first instruction, the second instruction, and the third instruction. I can't remember an endgame as extensive and many-layered, at least for a long while.