Okay, so putting yours and your wife's documents together, I would go with:
Jul-18 1. Wife: 27-Jun NHS Letter (Source 1)
1. You: Water Bill (Source 2)
Nov-18 2. Wife: NHS Letter
2. You: Bank Statement (Source 3)
Mar-19 3. Joint: 2019 Council Tax (Source 4)
Jul-19 4. Wife: NHS Letter
4. You: Bank StatementNov-195. Wife: Government Background Check (Source 5)
5. You: Bank StatementMar-20 6. Joint: 2020 Council Tax Letter Jul-207. Your wife: ?
7. You: ? So we can't seem to find documentation for July 2018 for my wife. I'm still looking for some. She has online banking but I assume that needs extra work on getting any bank statement countersigned.
You can only use documents that were physically received in the post in July 2018. Getting a bank statement now would mean you could only use it for July 2020 evidence, not July 2018.
However, since her NHS letter is dated Jun 27th, it's only 4 days away from being July, so you should be okay to use it anyway.
I would advise she changes to paper statements for her banking so that she receives them in the post every month... that way, when you apply for ILR, she will have a mailed bank statement available for any month you need it.
Also, her visa expires 24 August. If I apply in August then would all the months above be extended by 1 month? So Jul-18 become Aug-18.
No, you wouldn't need to change anything, just use July 2018 to July 2020.