SPOILER WARNING: The significance of "253" and a possible explanation for Good Cooper's amnesia
I apologize for the fragmented nature of my writing. These are all just hypotheses to test/build upon further:
"253 time and time again" - spoken by The Arm
25 years Laura Palmer sees agent Cooper again, then the 3 representing the 3 Coopers, hence "253"
15 is at first on the door then 3 later on when Ronette appears in the floaty space station.
2:53 on Ronette's wristwatch when leaving the lodge
2:52 changes to 2:53 on Ronette's watch - 2 changing to 3 represents the creation or realization by the lodge of another Cooper besides the Doppelgänger and Good Coop known as "Dougie"
(Nothing exists in real time in the lodge "is it future or is it past", so Dougie could have been created years ago, but in the lodge, it happens at this particular moment for Cooper to leave the lodge, maybe time rewinds when The Arm doppelgänger says "non-existence" so that it goes back to when Cooper was born to create another double of him, hence Cooper's reemergence from the lodge with a peculiar amnesia)
"non-existence" could just mean the total wipe of good Cooper's memory, especially because he does not recognize Ronette as familiar in the big tin can room. He would have asked just like in the case of asking if it was Laura Palmer earlier if he had the memory. Maybe this is just some malicious act by the dopplegangers to hinder goodness in the world.
5 golden shovels of Jacoby's
2 for good Dale and doppelganger
1 for Dougie doppelganger
5 pack of bunnies 2 left, one eaten by lucy long ago, so there were originally 3 when found
The one that's eaten represents Dougie being taken by the lodge as a doppelgänger substitute and transformed into a small gold pearl (this can work since again the lodge is outside of the constraints of time)
Gold has significance because of it's superior electrical conductivity
Gold is a way for the lodge spirits to manifest directly in the physical world because of it's superior conductivity as well as electronic devices which typically contain gold or maybe gold is involved in the creation of Dougie somehow?
I also saw those numbers throughout the episode. It was way later than I should have been awake so I'm rewatching tonight, but I thought I saw 235, 15, and 3. Those were all on placards of one kind or another. Add those up and you get 253, which like you had said was the time on Ronette's watch.
I didn't have the mental capacity at 1am to pull from it what you did, but thats what I'll be watching for a little later.
With regards to '253' in the Red Room with the Black/White zigzag (now unstable) floor, my guess is '25 years moment 3rd incidence':
1966/1967 events as studied by Project Blue Book establish the Black and White Lodge (incidence/opening up #1)
1991/1992 Earle versus Cooper Lodges open and close again (incidence #2)
2016/2017 window of opportunity for Cooper? (incidence #3)
Also, I saw an instagram story post by welcometotwinpeaks the other day that was eerily using the numbers 0, 1, 2, 3, 4, and 5. Maybe the social media manager of the site knows more than we do? It was a short video of Laura with the words "I'll see you again in 2 minutes and 0 seconds" with the "story" video ending at "2 minutes and 5 seconds" counting from 0-5 seconds. I may just be reading into this too much, but I thought it was post-worthy. Attached is a photo of what I am talking about.
I think it would be better to not extrapolate tenuous connections and jump at every instance of a potential connection without the full picture. A jigsaw cannot be complete without all of it's pieces.
An example of being tenuous is what you said here,
For me, this is nothing but drawing connections between things which aren't connected. It reminds me of the Half Life 3 memes which always tried to prove the existence of the game by making ludicrous additions and subtractions with irrelevant numbers and meanings. There is no reason, yet, to attach any connection between Jacoby's shovels and the multiple Coopers, but to then try and do some addition which fits your agenda appears as a fallacy.
""non-existence" could just mean the total wipe of good Cooper's memory, especially because he does not recognize Ronette as familiar in the big tin can room. "
He doesn't recognize Laura Palmer immediately, it's less likely he would have remembered Ronette's face, so the idea this causes his catatonic state doesn't fit well with me. I think the AC/DC theory for why Coopers brain/memories are scrambled. The non-existence line, for me, seemed to indicate a more metaphysical threat, than any real action by the doppleganger. Cooper is also somewhat coherent for the scenes following falling through the void, so it seems even more unlikely that the Doppletree did anything to him mentally or physically, apart from sending him into said void.