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def = "very expensive" (archaic slang) , wp = "strike" with L and A transposed

Temple like the kind you'd find in Cambodia, anag of ELGAR + L

Finally crawled, bloody and bruised, over the finish line, If this was 1994 I think I would call this one unfair, or at least "guess what Amicus is thinking." With the internet, enough of a hint was forming from the jumbles to try googling a few things. Still brutal. Looking back there are a few oblique hints in the clues that might send you looking in a certain direction, but hats off to the 8 who got this back in the day (I suspect they all were experts in the subject matter, to the point of having the relevant passages memorized!)

Thanks, all clues now solved.
How do you know how to enter the jumbles?
Which codes output double the number of letters of a word?

I do know 7 of the 8 letters in the encoded version of 1d and the same for 33a. 6 out of 8 for 4a and 19d

Bananabean, if you have eg 1d you have 3 of the encodings and half of 1. It's a straightforward first letter of the answer = first 2 of the letters in the grid. The problem arises with the second half of the half of one. If you know the code for the first letter of 1d you can enter the same for the start of 19d...the encoding is consistent throughout.

Thanks, Granama1, I have already done that which is why I know so many letters of the encoded entries.
There are a few spaces where this method fails me. I am also unsure of how to enter some of the jumbles but others are entered.

Ah, sorry, I realise I hadn't counted properly. How many letters do you have coding for, 7?

I know how to encode 4 letters fully but I know half of the code for the other 4

Bananabean, you need to make sense of the central area of the grid in order to provide a resolution to many of your jumbles. I think the letters in the clues to be encoded will sort the rest. You can assume that whenever a letter appears in those clues, it encodes to the same letter pair.

Doing that should direct you to where the solution to the encoding question is found

I ground through lots of options in the middle, looking for common letters and nibbling away at my mind was the puzzle title. These things tend to be symmetrical. I made a few assumptions (leaps of faith possibly!) about the jumbles. In the end something vaguely recognisable started to form.

Tbh I'm not sure that a completely methodical approach would resolve everything. I was held up for a long while though by thinking 23a must be 'tantalise'.

For completeness, I have attached a link to the solution.

SPOILER ALERT: Please don't click unless you wish to see it.

https://www.dropbox.com/scl/fi/cpwoe9vlm8e3zdnrlrqjo/Solution-to-Squaring-The-Circle.pdf?rlkey=iss92exe008ps5tcckckhs2yi&dl=0