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If you draw the lines with a ruler from the centre of blank cell to the centre of the corner cells it will pass through each relevant cell of the phrase even though for some of the cells, it is literally just grazing the edge

My take is that you are trying to carry out the title of the puzzle in a 2D way using the concept of the 15 letter phrase identified from the clues.

There are just 4 lines - one to each corner - and only two of the lines are required for the endgame but they have to be drawn very precisely and every cell they pass through (even by the tiniest bit) is involved in the phrase.

...sorry, that is misleading - only 2 are needed for the phrase, all 4 are needed to suggest the effect.

candledave - it's the extreme open-endedness of the gimmick that I have some issues with. Often we have other ways of limiting the possibilities - a given number, an additional thematic context, or just a limit per clue, here I think the setter has given himself just a bit too much leeway (something he didn't do with his other puzzle this week, which was far more 'user friendly', let's say).

That’s fair, the idea of more than one possible adjustment taken to the extreme I guess could lead to adding whole new sentences!

... and if you do use a very open-ended gimmick the clues really should be as unambiguous as possible to compensate (but as I've already gone for 'devious' instead of unfair, it's only a little quibble from me - I think it's a clever puzzle).

I like the 'whole new sentences' idea, candledave! There are setters who might fancy that.

Many thanks for that drxx and candledave. I will no doubt need more than one attempt to get the lines to touch a 'pixel' of each cell.

I have struggled to the finishing line. Thanks for all the hints.

Drxx describes the puzzle as devious. I’m not sure if this is a pejorative word to apply to a cryptic crossword! Unfortunately I think it is far worse than that.

To avoid extra letters in the four-word phrase, the line coming from the NW corner of the grid will have to pass precisely through the NW corner of the blank cell. So it will not meet the other line at the centre of the blank cell! The dot must therefore be placed nearer to the NW corner of the blank cell.

Is this devious? I would say unfair, or perhaps inappropriate for a puzzle like this.