This puzzle is also available as a spreadsheet here.
Transcription of some of the text:
FIRST STAGE OF PUZZLE
α BOGGLE
β VIZIER
γ ANGERS
δ TENDON
α LOSE
β POSTSCRIPTS
γ PURSUE
δ MISGIVINGS
α PANDA
β LIME
γ VANDALIZE
δ JAPANIMATION
α SPA
β WALES
γ PROTEIN
δ ANGLICAN
SECOND STAGE OF PUZZLE
FIFTY SQUARED MINUS FORTY-ONE (1, 2, 3, 4)
DOT AND CROSS YOURS (3, 1, 2, 4)
FIRST FIVE LETTERS' BITS (3, 4, 1, 2)
LEMME GET THIS STRAIGHT (4, 2, 3, ????, 1)
This puzzle requires some...
...FOUR-WORD THINKING! (A pun on 'forward-thinking'...)
For the first stage of the puzzle, each of the four columns of words (alpha through delta) needs to be matched to a different quadrant of the diagram before these four sub-puzzles can be solved.
FIRST STAGE OF PUZZLE
Sub-puzzle 1 (North-West corner):
α LOSE, β POSTSCRIPTS, γ PURSUE, δ MISGIVINGS
Each of these words has a synonym which is a compound word or phrase of two 'halves' (albeit of differing lengths). These halves can be positioned in the mini-grid, one to a square, with their lengths matching the enumeration shown. Then reading across the rows and columns gives us these synonyms:
α LOSE = COME SECOND
β POSTSCRIPTS = AFTERTHOUGHTS
γ PURSUE = COME AFTER
δ MISGIVINGS = SECOND THOUGHTS
The green boxes highlight our answer: AFTERTHOUGHTS
Sub-puzzle 2 (North-East corner):
α PANDA, β LIME, γ VANDALIZE, δ JAPANIMATION
We need to solve the relationship αβ : γ :: δ : ___. In other words, by working out how to get γ (VANDALIZE) from α (PANDA) and β (LIME), we can then derive the answer by applying the same transformation to δ.
It's a short step to see that [V]ANDALI[Z]E is derived by concatenating and changing P to V and M to Z in [P]ANDA and LI[M]E. What word can we make by changing these letters in 'JAPANIMATION'? That would be JAVANIZATION.
Sub-puzzle 3 (South-West corner):
α SPA, β WALES, γ PROTEIN, δ ANGLICAN
This sub-puzzle was my break-in to the whole puzzle. The number 189819 is very famous for a particular reason - it is the length in characters of the longest word in English: the full name of the protein also known as titin. A little thought made me realise that each of the words in this section clues a famously very long word:
SPA = Aequeosalinocalcalinoceraceoaluminosocupreovitriolic (describing the spa waters at Bath, England) [3,4];
WALES = Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch (a place in Wales) [3,7,4];
PROTEIN = Methionylthreonylthreonylglutaminylalanyl…isoleucine (the aforementioned protein) [3,189819];
ANGLICAN = Antidisestablishmentarianism (opposition to the disestablishment of the Anglican Church) [7,3].
If we interpret the numbers in square brackets as identifying letters at these numbered positions, we retrieve the letters QU, AIN, TE and ST, giving us the word QUAINTEST.
Sub-puzzle 4 (South-East corner):
α BOGGLE, β VIZIER, γ ANGERS, δ TENDON
Here we are looking for an 11-letter word that could be found via the rules of Boggle (moving from one adjacent letter to another to trace out a word), after assembling the other three words into a 3x6 rectangular grid:
VIZIER ANGERS TENDON
Beginning in the bottom-left corner, we can find the word TENDERIZING.
SECOND STAGE OF PUZZLE
For this stage, we must number our answer words as per the sub-puzzle number in my description above:
1 = AFTERTHOUGHTS
2 = JAVANIZATION
3 = QUAINTEST
4 = TENDERIZING
FIFTY SQUARED MINUS FORTY-ONE (1, 2, 3, 4)
The calculation results in the number 2459. If we position our words in the grid provided, repeatedly laying copies of the words side by side, ad infinitum, we get a grid that looks something like this:
If we read off the letters (downwards) that would be in the 2459th column, we would be able to spell the word FOUR (the 2nd letter of AFTERTHOUGHTS, the 11th of JAVANIZATION, the 2nd of QUAINTEST, and the 6th of TENDERIZING).
DOT AND CROSS YOURS (3, 1, 2, 4)
This is a reference to a well-known phrase about "dotting the i's and crossing the t's". If we extract all of the I's and T's from each word and replace each I with a dot and each T with a dash, we can generate some Morse code letters (a method hinted at by 'dot', of course):
QUA[.]N[-]ES[-], AF[-]ER[-]HOUGH[-]S, JAVAN[.]ZA[-][.]ON, [-]ENDER[.]Z[.]NG
i.e. .-- / --- / .-. / -..
This spells out the word WORD in Morse code.
FIRST FIVE LETTERS' BITS (3, 4, 1, 2)
(Thanks to @fljx for solving this part in comments)
Order the words as required and look at the 5 symbols given: '(', '—', '/', '\', and ')'. Now consider which of the first 5 letters in each word contain a segment ('bit') shaped (approximately) like each of these:
If we then treat the presence of one of these segments as a '1' and its absence as a '0' we can produce four 5-digit binary numbers (containing 'bits' of another kind!): 20, 8, 9 and 14. Using A1Z26, these numbers convert to letters to spell the word THIN.
LEMME GET THIS STRAIGHT (4, 2, 3, ????, 1)
The rectangles in this image strongly resemble playing cards. If we arrange the words in the given order - TENDERIZING, JAVANIZATION, QUAINTEST, ????, AFTERTHOUGHTS - we can see a pattern: each begins with a playing card in the sequential run of 10, Jack, Queen, [King], Ace (known as a 'straight' in poker). The missing card is our answer here: KING.
PUTTING THIS ALL TOGETHER:
Finally, these four words can now be concatenated to make the relevant phrase 'FOUR-WORD THINKING' (a play on words for 'forward thinking') - especially relevant since each starting set of words had four entries, and every phrase used in this puzzle, from 'FIRST/SECOND STAGE OF PUZZLE' right through to the four second-stage clues comprises precisely four words!
