While you may get away with home printed statements (people have done in the past), UKVI will know that this is what you have done and it's up to them whether they let it slide or not. Remember, they are experts in detecting forged documents so spotting the difference (say in print or paper quality) in home printed versus original statements will be a piece of cake for them.
Right okay, you may be right here. The only difference might be the paper quality but not being a document expert, I certainly can't tell the difference. Not worth the risk then. So this is the option I am leaning towards:
1. Send all documents to my wife in US. Including verified pay slips, stamped bank statements up until June.
2. Wait until 21st of July for bank statement to be released. Call the bank first thing in the morning (its a Saturday so documentation team might only be able to do this on the Monday). However, they can put the request in for me.
3. My wife submits her visa application on 21st of July, and books her bio metrics for 3rd of August (+-1day).
4. My bank verifies statement, first thing on Monday morning (23rd July) and sends them out first class.
5. I receive my statement by the 25th at the latest . I arrange a UPS collection on 26th of July for 3 day delivery. This means , my wife will have the final missing statement by 31st of July at the very latest. She can attend her appointment on 3rd of August.
Risks: - Statement may not reach their on time. In that case, if it doesn't arrive by 31st and we will cancel the bio metrics and apply for refund.
Now, does all of this sound feasible? This means my statement and last pay slip will be within 28 days limit. My employee letter is dated for 26/06/18 and letter from my landlord is dated for 03/07/18. So they will all be within 28 days as well. Assuming the 28 days is from application submission , then this works out.
We were not going to go with priority first, but we have changed our mind.