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Having started this thread I thought I should add a late update. I gave up on Sunday having hit the same block after restarting 3 times but unable to see my error.
Then I remembered in the early hours of Tuesday night that when I identified our special numbers a couple had more than one possible pair of squares as factors and I was using the wrong pair for 65.
Started again yesterday and slogged through the maths. The end game was very neat and overall it was a rewarding if grueling puzzle.
I have huge respect for Elap. Constructing one 5x5 grid with a dozen 5 letter words is remarkable. Constructing a second with the same letters is astonishing.
I can't imagine how to even start on constructing the mathematical element.

And a quick word in defense of the preamble. I could only find one possible word to complete the bottom row of the first grid and give 12 five letter words. So there is no ambiguity there.
There are however at least 2 possible solutions to the second grid. The top left letter could be T or G. Only one option gives a variation of the letters in first grid though.
The preamble is accurate - use the unambiguous first grid to remove ambiguity from the second grid - and leads to a unique correct solution to the puzzle.

I wasn't unhappy with the preamble either........but there is no letter G among the clues

Yes but there is nothing in the preamble to say the missing letters need to come from the the 10 coded letters.

Gem94, I wasn't happy with the preamble either. But this discussion of the letter G baffles me also. I have no G in either grid.

Smithsax - The second sentence of the second para says that 10 letters from the sequence .....replace the digits in both grids, so although taken in isolation a G could go where you say in the second grid and form words, there is no G in the sequence.

Sorry if I have caused confusion. I agree there is no letter G in the final solution. My point was that without this carefully worded preamble including a letter G in the top left position could have been regarded as correct. I was just supporting the compiler following earlier criticism of the preamble.

Very slow progress by me on this one - still struggling with the algebra. If anyone's still there, am I right in thinking that L + t = 78? Thanks for any help.

You are, but take care as there a couple of options for the individual values.

Many thanks, Crosswhit99: I have L = 17 and t = 61 (for the second time, the first time round led to impossibilities, so I'm not that optimistic that I'm on the right lines: confirmation or otherwise would be much appreciated).