Hi OP, I had a similar search recently. I finally got somewhere after years (first sale fell through). Towards the end, I did view some properties before they went onto the market (I think it was obvious how keen I was).
Are there estate agents at each local firm that you can reach out to to ask if there are any off-market sales coming up? It's also worth having instant alerts with Zoopla, Rightmove and Prime Location (just in case a property is not advertised at the same time on each of those platforms). I asked my employer for flexible working so that I could go to potential viewings asap (ideally that lunchtime or early evening).
Have you looked at Crystal Palace too?
When I bid on the property that I eventually completed on, I submitted: a mini bio (about me, how long I'd been saving, what I liked about the property and the local area); decision in principle; screenshot of deposit and legal expenses (with any sensitive info redacted); mortgage broker details, ID; and proof of address.
I mentioned that I already had a surveyor in mind (recommended by a colleague that had recently bought in the local area) and a conveyancer.
Worth checking anything that is 'back to market' after a purchase falls through - just in case the seller wants a quick sale.
Save any properties that you have a failed bid on (e.g. in 'My Rightmove') so you can see whether it goes back online.
Good luck, hope you find somewhere soon!