Nearly 4 days and only 1 reply. That's just sad

Let's see how things are going to be like with an additional incentive. That is in additional to the joy of learning and receiving some merits.
Alas, I only have little to give but now the key holds 0.00202000BTC. <- 3rd mystery!

@SFR10 Why not give the whole thing another read

I did not see that. I am obsessed with finding anagrams for "Even Santa owns bitcoin." and I only got this "bitcoin savant seen now". I guess I am wrong.

obviously. when in normal conversation people warm up their hands. but the OP strangely chose knuckles
instead of wood fire he chose kindling
instead of sit/lay/relax beside the fire he chose kneel..
instead of a wax candle.. kerosine
instead of a glass or a pitcher of eggnog. he chose keg of eggnog
seems to me he selectively chose words beginning with K that were okish replacements but not ones used in a normal conversation. thus it was obvious word replacement even without the Kones hint

BTW the coins still sit there unclaimed even though the puzzle is almost solved!

The wallet has no balance and transaction history.

https://www.blockchain.com/btc/address/14B3NsuKDk5piqnw71U9kDuSmvMJnYprnr

Am I viewing the address correctly?

--
My guess is the private key is composed of the corresponding number of the alphabet in the riddle. Let's say a=1 b=2 and so on. Then all "capital letters" are the letter in the private key itself. I'm using only mobile so it's hard for me to combine all numbers. 

It's actually the opposite - having two signatures with the same k allows you to compute k, and when you know k you go straight to extracting private key. So, when you already know k, one message is enough.

This is a really fun challange, I'm kinda stuck right now with my solution, but I already made some progress and learned a bit about ECDSA and Bitcoin, so even if I won't win, I'm already happy and I don't think the time I've spent is wasted.

Edit:

So, I've found a key, it resolves to a different address but the signature with k = 2020 is (almost, aside from recid) the same as the challenge:


Edit2: I think I understand what you did - you took a private key, signed a message with it, then switched the recid in the signature to lead to another public key, which you then also replaced in the signature. Is this correct? Though I still can't find any address with balance that corresponds to the private key that I found.

Now I only need to find what to do with this private key...

Done! https://www.blockchain.com/btc/tx/a198aa79ed1dee8cc4f7501b000c8d9ef373aad826d4fa1bc15990d32e303c77 -> https://www.blockchain.com/btc/tx/9521384c888e5a91c579378728df9808427e4da4f5c7373f527efb79794b64e9

(bumped the fee)

I imported it in Electrum with p2wpkh flag, worked like a charm!

Here is how you should have solved the puzzle.
We have
- the ECDSA equation ([1])
- Base64 signature with a recid so we had:
  - r = 0x37bb22d3f7afe8668e9b28561332d9e3734a8139bfe139d2c094741456403609
  - s = 0x50ca4a3efdeb86e9252b4c32114d77ae71911f4f5ed3ce13e5f82bdfd30658ab
  - v = 0x01
- z aka e is calculated easily from the message: 0xfb917a8e7c3dd70b329d7671cc388329749f5e90a39b7f2670a1311e90bb516a
- k = 2020

Also the above equation could be changed to by knowing the basic properties of modular arithmetic:
s*k=z+rd_A (mod n) => s*k - z = rd_A (mod n) => (s*k - z)r^-1 = d_A (mod n)

First thing to know is that all of the above is "modular arithmetic" so x^-1 or 1/x is not as simple as 1 divided by x. It is modular multiplicative inverse. That means 1/2 (mod n) is not 0.5 but instead it is 57896044618658097711785492504343953926418782139537452191302581570759080747169
ModInverse() method is found in all cryptography libraries.

With that we can calculate d_A (that is the private key) as
But if you get the P2PKH address from this key you'll get 1CNvS7ivEFrZWSbSSSc6fvQFgY7KNG16Aq (compressed pubkey) or as hatshepsut93 found 13LDi5Sb5YG2MAebUNkAB58t1DcFPCAaxZ (uncompressed pubkey).
By the way when redid-27 is bigger than 4 that means the compressed public key was used.

So something must have been wrong. It takes us back to recid. recid-27 is 5 and when you subtract 4 (the fixed value added to indicate compressed public key) you'll get 1. This could be an indication that negative s was used instead.
As I posted above, In bitcoin to prevent malleability there is a consensus rule that mandates usage of low S values in signatures. Which is basically a simple modular subtraction.

With the new (s = secp256k1.N - s) we get a new key value:
Now if you get the P2PKH address of this key you'll get 14B3NsuKDk5piqnw71U9kDuSmvMJnYprnr which is the correct address.

But where is the reward?
A single private key corresponds to a single public key point and from that public key you can create multiple script types (for simplicity addresses) one of which is P2WPKH which is known as a native SegWit address.

And the final "mystery" was that if you look at the private key posted here more closely or with another "eye" you can see that it is a simple human readable string! All you have to do is to convert the base58 or base16 to UTF8 to get: