PSE Advent Calendar 2023 (Day 24): ... and a Kappa Nu Year!

Question

<sub>This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2023. The accepted answer to this question will be awarded a bounty worth 250 reputation.

< Previous Door</sub>

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αββββγγγγγγγδδδδδδδδεεζζζζζζζηηηηηηηηθθ!
ιιιιιικκλλλλλλλλμμμννννννννννννξξοοοππππππρρρρρρρρσσσσττττ!
υυυυυφφφφφφφφφ...

... and a Kappa Nu Year!

Solve with Penpa+ (no answer check)

Across
1. Theme of the third Sunday in Pi
4. A 3 down of related programs, such as java.util, which contains List, Random, and Rho, among others
8. Be omicron cause of
10. Suffix added to theta across to form the name of a holiday
12. Like lambda under the age of 18 (in most countries)?
14. What the 55 in "I Beta Drive 55" is measured in (abbr.)
15. He painted Upsilon Christmas and a Happy New Year in '55
17. Kurdish city xi northern Iraq
19. 2009 platformer featuring a character who moves around iota to its own vomit
22. ___'easter, a powerful storm that most often occurs between Eta and March
23/25. Man whose birthday will be widely celebrated delta (!)
26. Sigma snake is said to have caused Cleopatra's death
27. Record company that released Whitney Houston's "Alpha Will Always Love You"
30. Something all members of a group gamma
31. Greek mythological king mu was bound to a wheel of fire
33. ___ Santa, 2003 Phi movie starring Billy Bob Thornton
35. Sleigh-riders have nu in this annual event since 1973
37. This rating epsilon a measure of the efficacy of sunscreen (abbr.)
38. Kappa disinfect or decontaminate
39. These were named as Rhode Island's state shell in the tau 1987
40. ___ judicata, Latin for "a matter zeta judged"

Down
1. Demi Lovato's new fiancé
2. A long continuous take, in TV and movie slang
3. The word with the most definitions in the OED, at 430 (not counting this one)
4. Stood up for
5. Going back and forth
6. Mitchell of Good Burger fame
7. Parent company of Old Navy and Banana Republic
9. Name for a group of First Nations people in northern Canada
11. Like the wool of a recently-fleeced sheep
13. Affliction caused by inflammation
14. Having very little wear?
16. Moved through the water
18. Show with a large sum of money involved
20. It can be really annoying
21. Brand of sugary food
23. There are two in an aperture
24. Took off
28. Apple software released one day before the death of Steve Jobs
29. Mountain range featuring the world's tallest volcanoes
32. Seep
34. Member of the Nahasapeemapetilon family
35. A sort of suffix
36. Quad bike (abbr.)

Answer 1

Solved crossword:

In each clue, a word has been replaced by a Greek letter. By...

backtracking from the solutions to the clues to figure out the words then putting them in the intro text (which also provides the lengths of each word and their order) the following phrase is uncovered:

I can't believe tomorrow is already December 25!
Thanks to everybody who participated in the Advent calendar this year!
Merry Christmas ... and a Kappa Nu Year!

However, there's more to this puzzle. In addition, I originally had trouble with 23/25 across because...

ISAAC NEWTON fits there as well! Apparently this also fits with 10A, but I had never heard of Newtonmas (thanks Stiv!) which really threw me for a loop.

Relevant clues:

4. Stood up for = PROTESTED/PROTECTED
5. Going back and forth = ALTERCATING/ALTERNATING
11. Like the wool of a recently-fleeced sheep = SHORT/SHORN
13. Affliction caused by inflammation = ARTHRITIS/ARTERITIS
14. Having very little wear? = MINI (as in size)/MINT (as in brand-new condition)
16. Moved through the water = SWUM/SWAM
18. Show with a large sum of money involved = LOST/LOOT
20. It can be really annoying = PEST/PSST
21. Brand of sugary food = TRIX/TWIX
23. There are two in an aperture = JAMBS/IAMBS ("an AperTURE")
24. Took off = SPED/APED