Waking up and confirming yesterday was not in fact a dream was a wonderful start to the day indeed!
As promised, the part I initially neglected to mention circles around our accidental omission of Appendix 2 in our submission of documents to Sheffield.
We received the email requesting the document on the same day we received confirmation our documents were with the UKVI. We could not believe that we had forgotten to include this (somewhat relieved by subsequently seeing so much mention of others getting asked for it - evidently one of the most common errors), so we scrambled while I was still in New York with my wife to scan the handwritten document in and send it through, which we accomplished on the same day rather than waiting 10 working days as mentioned in the email.
Following this, and after temporarily parting ways as I flew back, we only then realised we had only sent my payslips for my work - not a single letter-headed or stamped bank statement was included, and we had even somehow omitted the employer letter (continuing our strong start since forgetting Appendix 2).
As 10 days had not yet passed since we were asked for A2, I scrambled together the past year and half's worth of bank statements and asked my employer to write a suitable letter, both of which we emailed in desparation to the UKVI. We knew of their official stance of not accepting documents they do not ask for, and indeed aside from asking for A2, no mention was made of anything else.
We managed to get in touch with the centre directly, albeit a different department. After explaining our situation and after much pleading, my amazing wife managed to convince the person we contacted to leave a note to the settlement visa team to check their emails for documents relevant to A2 (as both things we sent were related to my job in someway). We asked for email confirmation to make sure everything was received, but not hear back.
After agonising over whether or not our documents were actually taken into consideration, we phoned again on Friday May 18th. Speaking to a different member of staff, we were informed that after checking on their systems they could see that our recently emailed documents were attached and will be taken into account. We were ecstatic at the news, as for us, and after what we'd read, having those attached was the difference between potentially being refused to potentially being ok.
More and more however we began to read of how often those not in the settlement department get things wrong, or give misinformation. This really started to hit us hard, and we weren't sure where we stood. And given the terrible delays this year, we didn't know when we could see each other again, as I had expended my full year's worth of work holidays already.
The rest is history though, and we were approved after convincing ourselves it was completely up in the air, which it may well have been until we did what we did, but our efforts paid off. The best of luck to anyone waiting for their result or to see what it is!!